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class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=%ED%8A%B9%EC%88%98:%EA%B3%84%EC%A0%95%EB%A7%8C%EB%93%A4%EA%B8%B0&returnto=%EB%8B%A4%EA%B0%81%EC%88%98" title="계정을 만들고 로그인하는 것이 좋습니다. 하지만 필수는 아닙니다" class=""><span>계정 만들기</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=%ED%8A%B9%EC%88%98:%EB%A1%9C%EA%B7%B8%EC%9D%B8&returnto=%EB%8B%A4%EA%B0%81%EC%88%98" title="위키백과에 로그인하면 여러가지 편리한 기능을 사용할 수 있습니다. [o]" accesskey="o" class=""><span>로그인</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="더 많은 옵션" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="개인 도구" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">개인 도구</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="사용자 메뉴" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=ko.wikipedia.org&uselang=ko"><span>기부</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%ED%8A%B9%EC%88%98:%EA%B3%84%EC%A0%95%EB%A7%8C%EB%93%A4%EA%B8%B0&returnto=%EB%8B%A4%EA%B0%81%EC%88%98" title="계정을 만들고 로그인하는 것이 좋습니다. 하지만 필수는 아닙니다"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>계정 만들기</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%ED%8A%B9%EC%88%98:%EB%A1%9C%EA%B7%B8%EC%9D%B8&returnto=%EB%8B%A4%EA%B0%81%EC%88%98" title="위키백과에 로그인하면 여러가지 편리한 기능을 사용할 수 있습니다. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>로그인</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> 로그아웃한 편집자를 위한 문서 <a href="/wiki/%EB%8F%84%EC%9B%80%EB%A7%90:%EC%86%8C%EA%B0%9C" aria-label="편집에 관해 더 알아보기"><span>더 알아보기</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/%ED%8A%B9%EC%88%98:%EB%82%B4%EA%B8%B0%EC%97%AC" title="이 IP 주소의 편집 목록 [y]" accesskey="y"><span>기여</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/%ED%8A%B9%EC%88%98:%EB%82%B4%EC%82%AC%EC%9A%A9%EC%9E%90%ED%86%A0%EB%A1%A0" title="현재 사용하는 IP 주소에 대한 토론 문서 [n]" accesskey="n"><span>토론</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="사이트"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="목차" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">목차</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">사이드바로 이동</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">숨기기</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">처음 위치</div> </a> </li> <li id="toc-정의" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#정의"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>정의</span> </div> </a> <ul id="toc-정의-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-성질" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#성질"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>성질</span> </div> </a> <button aria-controls="toc-성질-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>성질 하위섹션 토글하기</span> </button> <ul id="toc-성질-sublist" class="vector-toc-list"> <li id="toc-점화식" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#점화식"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>점화식</span> </div> </a> <ul id="toc-점화식-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-생성_함수" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#생성_함수"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>생성 함수</span> </div> </a> <ul id="toc-생성_함수-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-페르마_다각수_정리" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#페르마_다각수_정리"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>페르마 다각수 정리</span> </div> </a> <ul id="toc-페르마_다각수_정리-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-예" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#예"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>예</span> </div> </a> <button aria-controls="toc-예-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>예 하위섹션 토글하기</span> </button> <ul id="toc-예-sublist" class="vector-toc-list"> <li id="toc-평면도형수" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#평면도형수"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>평면도형수</span> </div> </a> <ul id="toc-평면도형수-sublist" class="vector-toc-list"> <li id="toc-중심있는_평면도형수" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#중심있는_평면도형수"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.1</span> <span>중심있는 평면도형수</span> </div> </a> <ul id="toc-중심있는_평면도형수-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-입체도형수" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#입체도형수"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>입체도형수</span> </div> </a> <ul id="toc-입체도형수-sublist" class="vector-toc-list"> <li id="toc-다면체수" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#다면체수"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2.1</span> <span>다면체수</span> </div> </a> <ul id="toc-다면체수-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-다포체수" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#다포체수"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2.2</span> <span>다포체수</span> </div> </a> <ul id="toc-다포체수-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-역사" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#역사"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>역사</span> </div> </a> <ul id="toc-역사-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-같이_보기" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#같이_보기"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>같이 보기</span> </div> </a> <ul id="toc-같이_보기-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-외부_링크" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#외부_링크"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>외부 링크</span> </div> </a> <ul id="toc-외부_링크-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="목차" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="목차" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="목차 토글" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">목차 토글</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">다각수</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="다른 언어로 문서를 방문합니다. 27개 언어로 읽을 수 있습니다" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-27" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">27개 언어</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B9%D8%AF%D8%AF_%D9%85%D8%B6%D9%84%D8%B9%D9%8A" title="عدد مضلعي – 아랍어" lang="ar" hreflang="ar" data-title="عدد مضلعي" data-language-autonym="العربية" data-language-local-name="아랍어" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Nombre_poligonal" title="Nombre poligonal – 카탈로니아어" lang="ca" hreflang="ca" data-title="Nombre poligonal" data-language-autonym="Català" data-language-local-name="카탈로니아어" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Polygonalzahl" title="Polygonalzahl – 독일어" lang="de" hreflang="de" data-title="Polygonalzahl" data-language-autonym="Deutsch" data-language-local-name="독일어" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-eml mw-list-item"><a href="https://eml.wikipedia.org/wiki/N%C3%B9mer_poligon%C3%A8l" title="Nùmer poligonèl – Emiliano-Romagnolo" lang="egl" hreflang="egl" data-title="Nùmer poligonèl" data-language-autonym="Emiliàn e rumagnòl" data-language-local-name="Emiliano-Romagnolo" class="interlanguage-link-target"><span>Emiliàn e rumagnòl</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Polygonal_number" title="Polygonal number – 영어" lang="en" hreflang="en" data-title="Polygonal number" data-language-autonym="English" data-language-local-name="영어" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Plurlatera_nombro" title="Plurlatera nombro – 에스페란토어" lang="eo" hreflang="eo" data-title="Plurlatera nombro" data-language-autonym="Esperanto" data-language-local-name="에스페란토어" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/N%C3%BAmero_poligonal" title="Número poligonal – 스페인어" lang="es" hreflang="es" data-title="Número poligonal" data-language-autonym="Español" data-language-local-name="스페인어" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Zenbaki_poligonal" title="Zenbaki poligonal – 바스크어" lang="eu" hreflang="eu" data-title="Zenbaki poligonal" data-language-autonym="Euskara" data-language-local-name="바스크어" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Monikulmioluku" title="Monikulmioluku – 핀란드어" lang="fi" hreflang="fi" data-title="Monikulmioluku" data-language-autonym="Suomi" data-language-local-name="핀란드어" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Nombre_polygonal" title="Nombre polygonal – 프랑스어" lang="fr" hreflang="fr" data-title="Nombre polygonal" data-language-autonym="Français" data-language-local-name="프랑스어" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%A1%D7%A4%D7%A8_%D7%9E%D7%A6%D7%95%D7%9C%D7%A2" title="מספר מצולע – 히브리어" lang="he" hreflang="he" data-title="מספר מצולע" data-language-autonym="עברית" data-language-local-name="히브리어" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Soksz%C3%B6gsz%C3%A1mok" title="Sokszögszámok – 헝가리어" lang="hu" hreflang="hu" data-title="Sokszögszámok" data-language-autonym="Magyar" data-language-local-name="헝가리어" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Bilangan_poligonal" title="Bilangan poligonal – 인도네시아어" lang="id" hreflang="id" data-title="Bilangan poligonal" data-language-autonym="Bahasa Indonesia" data-language-local-name="인도네시아어" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Poligona_nombro" title="Poligona nombro – 이도어" lang="io" hreflang="io" data-title="Poligona nombro" data-language-autonym="Ido" data-language-local-name="이도어" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Numero_poligonale" title="Numero poligonale – 이탈리아어" lang="it" hreflang="it" data-title="Numero poligonale" data-language-autonym="Italiano" data-language-local-name="이탈리아어" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%A4%9A%E8%A7%92%E6%95%B0" title="多角数 – 일본어" lang="ja" hreflang="ja" data-title="多角数" data-language-autonym="日本語" data-language-local-name="일본어" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Veelhoeksgetal" title="Veelhoeksgetal – 네덜란드어" lang="nl" hreflang="nl" data-title="Veelhoeksgetal" data-language-autonym="Nederlands" data-language-local-name="네덜란드어" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Polygontall" title="Polygontall – 노르웨이어(보크말)" lang="nb" hreflang="nb" data-title="Polygontall" data-language-autonym="Norsk bokmål" data-language-local-name="노르웨이어(보크말)" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/N%C3%BAmero_poligonal" title="Número poligonal – 포르투갈어" lang="pt" hreflang="pt" data-title="Número poligonal" data-language-autonym="Português" data-language-local-name="포르투갈어" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Num%C4%83r_poligonal" title="Număr poligonal – 루마니아어" lang="ro" hreflang="ro" data-title="Număr poligonal" data-language-autonym="Română" data-language-local-name="루마니아어" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru badge-Q70894304 mw-list-item" title=""><a 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class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">사이드바로 이동</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">숨기기</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">위키백과, 우리 모두의 백과사전.</div> </div> <div id="contentSub"><div id="mw-content-subtitle"><span class="mw-redirectedfrom">(<a href="/w/index.php?title=%EC%A4%91%EC%8B%AC%EC%9E%88%EB%8A%94_%EC%9C%A1%EA%B0%81%EC%88%98&redirect=no" class="mw-redirect" title="중심있는 육각수">중심있는 육각수</a>에서 넘어옴)</span></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="ko" dir="ltr"><p><span class="nowrap"></span> <a href="/wiki/%EC%88%98%ED%95%99" title="수학">수학</a>에서 <b>다각수</b>(多角數, <span style="font-size: smaller;"><a href="/wiki/%EC%98%81%EC%96%B4" title="영어">영어</a>: </span><span lang="en">polygonal number</span>)는 <a href="/wiki/%EC%82%BC%EA%B0%81%EC%88%98" title="삼각수">삼각수</a>와 <a href="/wiki/%EC%A0%95%EC%82%AC%EA%B0%81%EC%88%98" title="정사각수">정사각수</a>를 임의의 <a href="/wiki/%EC%A0%95%EB%8B%A4%EA%B0%81%ED%98%95" title="정다각형">정다각형</a>에까지 일반화하여 얻는 평면 <a href="/w/index.php?title=%EB%8F%84%ED%98%95%EC%88%98&action=edit&redlink=1" class="new" title="도형수 (없는 문서)">도형수</a>이다. 기하학적으로, 다각수는 정다각형에 배열된 공의 수를 나타낸다. 주어진 다각수 바로 다음에 오는 다각수를 얻으려면 다각형의 이웃하는 두 변의 길이를 늘려 원래와 <a href="/wiki/%EB%8B%AE%EC%9D%8C_(%EA%B8%B0%ED%95%98%ED%95%99)" title="닮음 (기하학)">닮은</a> 새로운 다각형으로 확장하면 된다. 이 경우 늘리려는 두 변에 각각 한 개의 공이 추가되며, 새로운 다각형의 남은 변을 만들기 위한 공들 역시 추가된다. 이렇게 추가되는 부분을 다각수의 그노몬(<span style="font-size: smaller;"><a href="/wiki/%EC%98%81%EC%96%B4" title="영어">영어</a>: </span><span lang="en">gnomon</span>)이라고 부른다. 대수학적으로, 다각수는 1에서 시작하는 자연수 공차의 <a href="/wiki/%EB%93%B1%EC%B0%A8_%EC%88%98%EC%97%B4" class="mw-redirect" title="등차 수열">등차 수열</a>의 <a href="/wiki/%EB%B6%80%EB%B6%84%ED%95%A9" class="mw-redirect" title="부분합">부분합</a>을 나타내며, 그노몬은 이 등차 수열의 각 항에 대응한다 </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="정의"><span id=".EC.A0.95.EC.9D.98"></span>정의</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EB%8B%A4%EA%B0%81%EC%88%98&action=edit&section=1" title="부분 편집: 정의"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>자연수 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m\geq 3}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <mo>≥</mo> <mn>3</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m\geq 3}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4610f29d2708d1febf1c0090f58ddd3986593545" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:6.301ex; height:2.343ex;" alt="{\displaystyle m\geq 3}"></span> 및 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span>이 주어졌을 때, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span>번째 <b><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07d98bb302f3856cbabc47b2b9016692e3f7bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.04ex; height:1.676ex;" alt="{\displaystyle m}"></span>각수</b>(<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07d98bb302f3856cbabc47b2b9016692e3f7bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.04ex; height:1.676ex;" alt="{\displaystyle m}"></span>角數, <span style="font-size: smaller;"><a href="/wiki/%EC%98%81%EC%96%B4" title="영어">영어</a>: </span><span lang="en"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07d98bb302f3856cbabc47b2b9016692e3f7bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.04ex; height:1.676ex;" alt="{\displaystyle m}"></span>-gonal number</span>) <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \operatorname {Pol} (m;n)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Pol</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>m</mi> <mo>;</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \operatorname {Pol} (m;n)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/53a35a2eebf23d8e21e98120da96139f10a9a014" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.67ex; height:2.843ex;" alt="{\displaystyle \operatorname {Pol} (m;n)}"></span>은 다음과 같이 정의된다. </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \operatorname {Pol} (m;n)=\sum _{k=0}^{n-1}(1+(m-2)k)={\frac {n((m-2)n-(m-4))}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Pol</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>m</mi> <mo>;</mo> <mi>n</mi> <mo stretchy="false">)</mo> <mo>=</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </munderover> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mo stretchy="false">(</mo> <mi>m</mi> <mo>−</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mi>k</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>n</mi> <mo stretchy="false">(</mo> <mo stretchy="false">(</mo> <mi>m</mi> <mo>−</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mi>n</mi> <mo>−</mo> <mo stretchy="false">(</mo> <mi>m</mi> <mo>−</mo> <mn>4</mn> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \operatorname {Pol} (m;n)=\sum _{k=0}^{n-1}(1+(m-2)k)={\frac {n((m-2)n-(m-4))}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d38438bab3627acc133535bcdcdb6d4a2c99967" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:58.079ex; height:7.509ex;" alt="{\displaystyle \operatorname {Pol} (m;n)=\sum _{k=0}^{n-1}(1+(m-2)k)={\frac {n((m-2)n-(m-4))}{2}}}"></span></dd></dl> <p>특히, </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \operatorname {Pol} (3;n)=n(n+1)/2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Pol</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>3</mn> <mo>;</mo> <mi>n</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>n</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \operatorname {Pol} (3;n)=n(n+1)/2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cbc1144a438187fa524114f3aa37c5babde16543" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:22.818ex; height:2.843ex;" alt="{\displaystyle \operatorname {Pol} (3;n)=n(n+1)/2}"></span>를 <b><a href="/wiki/%EC%82%BC%EA%B0%81%EC%88%98" title="삼각수">삼각수</a></b>라고 한다. 1~5번째 삼각수는 다음과 같다 (빨간색 부분은 그노몬을 나타낸다). <dl><dd><span typeof="mw:File"><a href="/wiki/%ED%8C%8C%EC%9D%BC:Polygonal_Number_3.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/69/Polygonal_Number_3.gif/600px-Polygonal_Number_3.gif" decoding="async" width="600" height="92" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/69/Polygonal_Number_3.gif/900px-Polygonal_Number_3.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/6/69/Polygonal_Number_3.gif 2x" data-file-width="1000" data-file-height="154" /></a></span></dd></dl></li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \operatorname {Pol} (4;n)=n^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Pol</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>4</mn> <mo>;</mo> <mi>n</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \operatorname {Pol} (4;n)=n^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/85a1a1e0fbada381ef1438fd56cdc9333ef6a8db" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.34ex; height:3.176ex;" alt="{\displaystyle \operatorname {Pol} (4;n)=n^{2}}"></span>를 <b><a href="/wiki/%EC%A0%95%EC%82%AC%EA%B0%81%EC%88%98" title="정사각수">정사각수</a></b>라고 한다. 1~5번째 사각수는 다음과 같다. <dl><dd><span typeof="mw:File"><a href="/wiki/%ED%8C%8C%EC%9D%BC:Polygonal_Number_4.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Polygonal_Number_4.gif/600px-Polygonal_Number_4.gif" decoding="async" width="600" height="103" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Polygonal_Number_4.gif/900px-Polygonal_Number_4.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/9/99/Polygonal_Number_4.gif 2x" data-file-width="1000" data-file-height="172" /></a></span></dd></dl></li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \operatorname {Pol} (5;n)=n(3n-1)/2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Pol</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>5</mn> <mo>;</mo> <mi>n</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>n</mi> <mo stretchy="false">(</mo> <mn>3</mn> <mi>n</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \operatorname {Pol} (5;n)=n(3n-1)/2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1cece0eba9d3fd1c44e1fab365d48e5289af09c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:23.98ex; height:2.843ex;" alt="{\displaystyle \operatorname {Pol} (5;n)=n(3n-1)/2}"></span>를 <b><a href="/wiki/%EC%98%A4%EA%B0%81%EC%88%98" title="오각수">오각수</a></b>라고 한다. 1~5번째 오각수는 다음과 같다. <dl><dd><span typeof="mw:File"><a href="/wiki/%ED%8C%8C%EC%9D%BC:Polygonal_Number_5.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/54/Polygonal_Number_5.gif/600px-Polygonal_Number_5.gif" decoding="async" width="600" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/54/Polygonal_Number_5.gif/900px-Polygonal_Number_5.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/5/54/Polygonal_Number_5.gif 2x" data-file-width="1000" data-file-height="250" /></a></span></dd></dl></li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \operatorname {Pol} (6;n)=n(2n-1)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Pol</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>6</mn> <mo>;</mo> <mi>n</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>n</mi> <mo stretchy="false">(</mo> <mn>2</mn> <mi>n</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \operatorname {Pol} (6;n)=n(2n-1)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7a644def273b47ecc24cb0e0c20ddd7438f37ee6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:21.655ex; height:2.843ex;" alt="{\displaystyle \operatorname {Pol} (6;n)=n(2n-1)}"></span>를 <b><a href="/wiki/%EC%9C%A1%EA%B0%81%EC%88%98_(%EC%88%98%ED%95%99)" title="육각수 (수학)">육각수</a></b>라고 한다. 1~5번째 육각수는 다음과 같다. <dl><dd><span typeof="mw:File"><a href="/wiki/%ED%8C%8C%EC%9D%BC:Polygonal_Number_6.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7a/Polygonal_Number_6.gif/600px-Polygonal_Number_6.gif" decoding="async" width="600" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7a/Polygonal_Number_6.gif/900px-Polygonal_Number_6.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/7/7a/Polygonal_Number_6.gif 2x" data-file-width="1000" data-file-height="250" /></a></span></dd></dl></li></ul> <div class="mw-heading mw-heading2"><h2 id="성질"><span id=".EC.84.B1.EC.A7.88"></span>성질</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EB%8B%A4%EA%B0%81%EC%88%98&action=edit&section=2" title="부분 편집: 성질"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="점화식"><span id=".EC.A0.90.ED.99.94.EC.8B.9D"></span>점화식</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EB%8B%A4%EA%B0%81%EC%88%98&action=edit&section=3" title="부분 편집: 점화식"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>다음과 같은 <a href="/wiki/%EC%A0%90%ED%99%94%EC%8B%9D" title="점화식">점화식</a>이 성립한다. </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \operatorname {Pol} (m;n+1)=\operatorname {Pol} (m;n)+(m-2)n+1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Pol</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>m</mi> <mo>;</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>=</mo> <mi>Pol</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>m</mi> <mo>;</mo> <mi>n</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mo stretchy="false">(</mo> <mi>m</mi> <mo>−</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \operatorname {Pol} (m;n+1)=\operatorname {Pol} (m;n)+(m-2)n+1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d8f886e28767943552b753d8617e7726a3f19e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:42.533ex; height:2.843ex;" alt="{\displaystyle \operatorname {Pol} (m;n+1)=\operatorname {Pol} (m;n)+(m-2)n+1}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="생성_함수"><span id=".EC.83.9D.EC.84.B1_.ED.95.A8.EC.88.98"></span>생성 함수</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EB%8B%A4%EA%B0%81%EC%88%98&action=edit&section=4" title="부분 편집: 생성 함수"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>다각수의 <a href="/wiki/%EC%83%9D%EC%84%B1_%ED%95%A8%EC%88%98" class="mw-redirect mw-disambig" title="생성 함수">생성 함수</a>는 다음과 같다. </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{n=0}^{\infty }\operatorname {Pol} (m;n)x^{n}={\frac {x((m-3)x+1)}{(1-x)^{3}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </munderover> <mi>Pol</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>m</mi> <mo>;</mo> <mi>n</mi> <mo stretchy="false">)</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>x</mi> <mo stretchy="false">(</mo> <mo stretchy="false">(</mo> <mi>m</mi> <mo>−</mo> <mn>3</mn> <mo stretchy="false">)</mo> <mi>x</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> <mrow> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <mi>x</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum _{n=0}^{\infty }\operatorname {Pol} (m;n)x^{n}={\frac {x((m-3)x+1)}{(1-x)^{3}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ab55e44adc2ce7955c769ac4ba0d96c45c0aba8e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:36.219ex; height:6.843ex;" alt="{\displaystyle \sum _{n=0}^{\infty }\operatorname {Pol} (m;n)x^{n}={\frac {x((m-3)x+1)}{(1-x)^{3}}}}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="페르마_다각수_정리"><span id=".ED.8E.98.EB.A5.B4.EB.A7.88_.EB.8B.A4.EA.B0.81.EC.88.98_.EC.A0.95.EB.A6.AC"></span>페르마 다각수 정리</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EB%8B%A4%EA%B0%81%EC%88%98&action=edit&section=5" title="부분 편집: 페르마 다각수 정리"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r34311305">.mw-parser-output .hatnote{}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}</style><div role="note" class="hatnote navigation-not-searchable"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/52/Icons8_flat_search.svg/18px-Icons8_flat_search.svg.png" decoding="async" width="18" height="18" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/52/Icons8_flat_search.svg/27px-Icons8_flat_search.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/52/Icons8_flat_search.svg/36px-Icons8_flat_search.svg.png 2x" data-file-width="512" data-file-height="512" /></span></span> 이 부분의 본문은 <a href="/wiki/%ED%8E%98%EB%A5%B4%EB%A7%88_%EB%8B%A4%EA%B0%81%EC%88%98_%EC%A0%95%EB%A6%AC" title="페르마 다각수 정리">페르마 다각수 정리</a>입니다.</div> <p>임의의 자연수는 많아도 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07d98bb302f3856cbabc47b2b9016692e3f7bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.04ex; height:1.676ex;" alt="{\displaystyle m}"></span>개의 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07d98bb302f3856cbabc47b2b9016692e3f7bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.04ex; height:1.676ex;" alt="{\displaystyle m}"></span>각수의 합으로 나타낼 수 있다. 즉, 임의의 자연수 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span>에 대하여, 다음을 만족시키는 자연수 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n_{1},\dots ,n_{m}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n_{1},\dots ,n_{m}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2d2c759120726280c1d6fee9e25e08a804576315" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.697ex; height:2.009ex;" alt="{\displaystyle n_{1},\dots ,n_{m}}"></span>이 존재한다. </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a=\sum _{k=1}^{m}\operatorname {Pol} (m;n_{k})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>=</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </munderover> <mi>Pol</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>m</mi> <mo>;</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a=\sum _{k=1}^{m}\operatorname {Pol} (m;n_{k})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/845781f6600837b85516d5137173a39b5f5416e1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:18.83ex; height:6.843ex;" alt="{\displaystyle a=\sum _{k=1}^{m}\operatorname {Pol} (m;n_{k})}"></span></dd></dl> <p>이를 <a href="/wiki/%ED%8E%98%EB%A5%B4%EB%A7%88_%EB%8B%A4%EA%B0%81%EC%88%98_%EC%A0%95%EB%A6%AC" title="페르마 다각수 정리">페르마 다각수 정리</a>라고 한다. (만약 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m'<m}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>m</mi> <mo>′</mo> </msup> <mo><</mo> <mi>m</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m'<m}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b938155755d2a56cb5b1a9531ce0036fffa74796" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.864ex; height:2.509ex;" alt="{\displaystyle m'<m}"></span>에 대하여 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>m</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b2ea8347f7588b19652c2098395f059d76b12b60" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.725ex; height:2.509ex;" alt="{\displaystyle m'}"></span>개의 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07d98bb302f3856cbabc47b2b9016692e3f7bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.04ex; height:1.676ex;" alt="{\displaystyle m}"></span>각수로 나타내려면 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n_{m'+1}=\cdots =n_{m}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>m</mi> <mo>′</mo> </msup> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mo>⋯</mo> <mo>=</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n_{m'+1}=\cdots =n_{m}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d33c1f573b86de349e6e6856a495d713d657e211" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:21.953ex; height:2.676ex;" alt="{\displaystyle n_{m'+1}=\cdots =n_{m}=0}"></span>을 취하면 된다.) </p> <div class="mw-heading mw-heading2"><h2 id="예"><span id=".EC.98.88"></span>예</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EB%8B%A4%EA%B0%81%EC%88%98&action=edit&section=6" title="부분 편집: 예"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="평면도형수"><span id=".ED.8F.89.EB.A9.B4.EB.8F.84.ED.98.95.EC.88.98"></span>평면도형수</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EB%8B%A4%EA%B0%81%EC%88%98&action=edit&section=7" title="부분 편집: 평면도형수"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>주어진 자연수 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 3\leq m\leq 30}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>3</mn> <mo>≤</mo> <mi>m</mi> <mo>≤</mo> <mn>30</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 3\leq m\leq 30}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/50f7cf6c9c9bdcd0fcc458801396520e811113b8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:11.725ex; height:2.343ex;" alt="{\displaystyle 3\leq m\leq 30}"></span>에 대하여, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07d98bb302f3856cbabc47b2b9016692e3f7bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.04ex; height:1.676ex;" alt="{\displaystyle m}"></span>각수는 다음과 같다. </p> <table class="wikitable"> <tbody><tr> <th><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07d98bb302f3856cbabc47b2b9016692e3f7bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.04ex; height:1.676ex;" alt="{\displaystyle m}"></span> </th> <th>명칭 </th> <th><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \operatorname {Pol} (m;n)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Pol</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>m</mi> <mo>;</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \operatorname {Pol} (m;n)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/53a35a2eebf23d8e21e98120da96139f10a9a014" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.67ex; height:2.843ex;" alt="{\displaystyle \operatorname {Pol} (m;n)}"></span> </th> <th>처음 20항 (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 0\leq n\leq 19}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>0</mn> <mo>≤</mo> <mi>n</mi> <mo>≤</mo> <mn>19</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 0\leq n\leq 19}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/96b669c6902e194956b5b019ab0f561518b1b733" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:11.079ex; height:2.343ex;" alt="{\displaystyle 0\leq n\leq 19}"></span>) </th> <th>OEIS </th></tr> <tr> <td>3 </td> <td><a href="/wiki/%EC%82%BC%EA%B0%81%EC%88%98" title="삼각수">삼각수</a> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n(n+1)/2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n(n+1)/2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/880739d44f2dc75cf0c9404a2d4b984f1fbc610a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.926ex; height:2.843ex;" alt="{\displaystyle n(n+1)/2}"></span> </td> <td>0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, ... </td> <td><a href="//oeis.org/A000217" class="extiw" title="oeis:A000217">A000217</a> </td></tr> <tr> <td>4 </td> <td><a href="/wiki/%EC%A0%95%EC%82%AC%EA%B0%81%EC%88%98" title="정사각수">정사각수</a> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ac9810bbdafe4a6a8061338db0f74e25b7952620" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.449ex; height:2.676ex;" alt="{\displaystyle n^{2}}"></span> </td> <td>0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, ... </td> <td><a href="//oeis.org/A000290" class="extiw" title="oeis:A000290">A000290</a> </td></tr> <tr> <td>5 </td> <td><a href="/wiki/%EC%98%A4%EA%B0%81%EC%88%98" title="오각수">오각수</a> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n(3n-1)/2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo stretchy="false">(</mo> <mn>3</mn> <mi>n</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n(3n-1)/2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/191b8310b05e397be27fa0c95342fedc4928d31e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.089ex; height:2.843ex;" alt="{\displaystyle n(3n-1)/2}"></span> </td> <td>0, 1, 5, 12, 22, 35, 51, 70, 92, 117, 145, 176, 210, 247, 287, 330, 376, 425, 477, 532, ... </td> <td><a href="//oeis.org/A000326" class="extiw" title="oeis:A000326">A000326</a> </td></tr> <tr> <td>6 </td> <td><a href="/wiki/%EC%9C%A1%EA%B0%81%EC%88%98_(%EC%88%98%ED%95%99)" title="육각수 (수학)">육각수</a> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n(2n-1)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo stretchy="false">(</mo> <mn>2</mn> <mi>n</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n(2n-1)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3520a349efff24865a3ea825ae26836a8db7d688" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.764ex; height:2.843ex;" alt="{\displaystyle n(2n-1)}"></span> </td> <td>0, 1, 6, 15, 28, 45, 66, 91, 120, 153, 190, 231, 276, 325, 378, 435, 496, 561, 630, 703, ... </td> <td><a href="//oeis.org/A000384" class="extiw" title="oeis:A000384">A000384</a> </td></tr> <tr> <td>7 </td> <td>칠각수(七角數, <span style="font-size: smaller;"><a href="/wiki/%EC%98%81%EC%96%B4" title="영어">영어</a>: </span><span lang="en">heptagonal number</span>) </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n(5n-3)/2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo stretchy="false">(</mo> <mn>5</mn> <mi>n</mi> <mo>−</mo> <mn>3</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n(5n-3)/2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ae237aac07bc4d29ca08a97e605aeecf2f7c4a46" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.089ex; height:2.843ex;" alt="{\displaystyle n(5n-3)/2}"></span> </td> <td>0, 1, 7, 18, 34, 55, 81, 112, 148, 189, 235, 286, 342, 403, 469, 540, 616, 697, 783, 874, ... </td> <td><a href="//oeis.org/A000566" class="extiw" title="oeis:A000566">A000566</a> </td></tr> <tr> <td>8 </td> <td><a href="/wiki/%ED%8C%94%EA%B0%81%EC%88%98" title="팔각수">팔각수</a> </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n(3n-2)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo stretchy="false">(</mo> <mn>3</mn> <mi>n</mi> <mo>−</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n(3n-2)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/632d236171de8bc2148c81071b0a848e5a649779" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.764ex; height:2.843ex;" alt="{\displaystyle n(3n-2)}"></span> </td> <td>0, 1, 8, 21, 40, 65, 96, 133, 176, 225, 280, 341, 408, 481, 560, 645, 736, 833, 936, 1045, </td> <td><a href="//oeis.org/A000567" class="extiw" title="oeis:A000567">A000567</a> </td></tr> <tr> <td>9 </td> <td>구각수(九角數, <span style="font-size: smaller;"><a href="/wiki/%EC%98%81%EC%96%B4" title="영어">영어</a>: </span><span lang="en">nonagonal number</span>) </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n(7n-5)/2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo stretchy="false">(</mo> <mn>7</mn> <mi>n</mi> <mo>−</mo> <mn>5</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n(7n-5)/2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/014c1459de53095ce51e3be53974e0e58a5040d2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.089ex; height:2.843ex;" alt="{\displaystyle n(7n-5)/2}"></span> </td> <td>0, 1, 9, 24, 46, 75, 111, 154, 204, 261, 325, 396, 474, 559, 651, 750, 856, 969, 1089, 1216, ... </td> <td><a href="//oeis.org/A001106" class="extiw" title="oeis:A001106">A001106</a> </td></tr> <tr> <td>10 </td> <td>십각수(十角數, <span style="font-size: smaller;"><a href="/wiki/%EC%98%81%EC%96%B4" title="영어">영어</a>: </span><span lang="en">decagonal number</span>) </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n(4n-3)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo stretchy="false">(</mo> <mn>4</mn> <mi>n</mi> <mo>−</mo> <mn>3</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n(4n-3)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c4a09e15b8068370e111ca77e7ae29c684b88e50" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.764ex; height:2.843ex;" alt="{\displaystyle n(4n-3)}"></span> </td> <td>0, 1, 10, 27, 52, 85, 126, 175, 232, 297, 370, 451, 540, 637, 742, 855, 976, 1105, 1242, 1387, ... </td> <td><a href="//oeis.org/A001107" class="extiw" title="oeis:A001107">A001107</a> </td></tr> <tr> <td>11 </td> <td>십일각수(十一角數, <span style="font-size: smaller;"><a href="/wiki/%EC%98%81%EC%96%B4" title="영어">영어</a>: </span><span lang="en">hendecagonal number</span>) </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n(9n-7)/2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo stretchy="false">(</mo> <mn>9</mn> <mi>n</mi> <mo>−</mo> <mn>7</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n(9n-7)/2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2f979994a6ab7c8ab3192cb4f7b93935b00de245" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.089ex; height:2.843ex;" alt="{\displaystyle n(9n-7)/2}"></span> </td> <td>0, 1, 11, 30, 58, 95, 141, 196, 260, 333, 415, 506, 606, 715, 833, 960, 1096, 1241, 1395, 1558, ... </td> <td><a href="//oeis.org/A051682" class="extiw" title="oeis:A051682">A051682</a> </td></tr> <tr> <td>12 </td> <td>십이각수(十二角數, <span style="font-size: smaller;"><a href="/wiki/%EC%98%81%EC%96%B4" title="영어">영어</a>: </span><span lang="en">dodecagonal number</span>) </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n(5n-4)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo stretchy="false">(</mo> <mn>5</mn> <mi>n</mi> <mo>−</mo> <mn>4</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n(5n-4)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/97146f05dedadcca62f56548d395575609cac849" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.764ex; height:2.843ex;" alt="{\displaystyle n(5n-4)}"></span> </td> <td>0, 1, 12, 33, 64, 105, 156, 217, 288, 369, 460, 561, 672, 793, 924, 1065, 1216, 1377, 1548, 1729, ... </td> <td><a href="//oeis.org/A051624" class="extiw" title="oeis:A051624">A051624</a> </td></tr> <tr> <td>13 </td> <td>십삼각수(十三角數, <span style="font-size: smaller;"><a href="/wiki/%EC%98%81%EC%96%B4" title="영어">영어</a>: </span><span lang="en">tridecagonal number</span>) </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n(11n-9)/2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo stretchy="false">(</mo> <mn>11</mn> <mi>n</mi> <mo>−</mo> <mn>9</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n(11n-9)/2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68e3e0047f44bcd0609f7576b3b28eb0c1340817" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.251ex; height:2.843ex;" alt="{\displaystyle n(11n-9)/2}"></span> </td> <td>0, 1, 13, 36, 70, 115, 171, 238, 316, 405, 505, 616, 738, 871, 1015, 1170, 1336, 1513, 1701, 1900, ... </td> <td><a href="//oeis.org/A051865" class="extiw" title="oeis:A051865">A051865</a> </td></tr> <tr> <td>14 </td> <td>십사각수(十四角數, <span style="font-size: smaller;"><a href="/wiki/%EC%98%81%EC%96%B4" title="영어">영어</a>: </span><span lang="en">tetradecagonal number</span>) </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n(6n-5)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo stretchy="false">(</mo> <mn>6</mn> <mi>n</mi> <mo>−</mo> <mn>5</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n(6n-5)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01249e25fd493247aee79b989434f3dfba402a9a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.764ex; height:2.843ex;" alt="{\displaystyle n(6n-5)}"></span> </td> <td>0, 1, 14, 39, 76, 125, 186, 259, 344, 441, 550, 671, 804, 949, 1106, 1275, 1456, 1649, 1854, 2071, ... </td> <td><a href="//oeis.org/A051866" class="extiw" title="oeis:A051866">A051866</a> </td></tr> <tr> <td>15 </td> <td>십오각수(十五角數, <span style="font-size: smaller;"><a href="/wiki/%EC%98%81%EC%96%B4" title="영어">영어</a>: </span><span lang="en">pentadecagonal number</span>) </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n(13n-11)/2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo stretchy="false">(</mo> <mn>13</mn> <mi>n</mi> <mo>−</mo> <mn>11</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n(13n-11)/2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/639aa7334e7a83350576f4a851c875740cfbde57" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.414ex; height:2.843ex;" alt="{\displaystyle n(13n-11)/2}"></span> </td> <td>0, 1, 15, 42, 82, 135, 201, 280, 372, 477, 595, 726, 870, 1027, 1197, 1380, 1576, 1785, 2007, 2242, ... </td> <td><a href="//oeis.org/A051867" class="extiw" title="oeis:A051867">A051867</a> </td></tr> <tr> <td>16 </td> <td>십육각수(十六角數, <span style="font-size: smaller;"><a href="/wiki/%EC%98%81%EC%96%B4" title="영어">영어</a>: </span><span lang="en">hexadecagonal number</span>) </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n(7n-6)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo stretchy="false">(</mo> <mn>7</mn> <mi>n</mi> <mo>−</mo> <mn>6</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n(7n-6)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/36820647761d3eb237f975a452a4b6bfa8b9d37b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.764ex; height:2.843ex;" alt="{\displaystyle n(7n-6)}"></span> </td> <td>0, 1, 16, 45, 88, 145, 216, 301, 400, 513, 640, 781, 936, 1105, 1288, 1485, 1696, 1921, 2160, 2413, ... </td> <td><a href="//oeis.org/A051868" class="extiw" title="oeis:A051868">A051868</a> </td></tr> <tr> <td>17 </td> <td>십칠각수(十七角數, <span style="font-size: smaller;"><a href="/wiki/%EC%98%81%EC%96%B4" title="영어">영어</a>: </span><span lang="en">heptadecagonal number</span>) </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n(15n-13)/2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo stretchy="false">(</mo> <mn>15</mn> <mi>n</mi> <mo>−</mo> <mn>13</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n(15n-13)/2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5c541228aed1aac506b2b6f5393c7992dbd3e60f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.414ex; height:2.843ex;" alt="{\displaystyle n(15n-13)/2}"></span> </td> <td>0, 1, 17, 48, 94, 155, 231, 322, 428, 549, 685, 836, 1002, 1183, 1379, 1590, 1816, 2057, 2313, 2584, ... </td> <td><a href="//oeis.org/A051869" class="extiw" title="oeis:A051869">A051869</a> </td></tr> <tr> <td>18 </td> <td>십팔각수(十八角數, <span style="font-size: smaller;"><a href="/wiki/%EC%98%81%EC%96%B4" title="영어">영어</a>: </span><span lang="en">octadecagonal number</span>) </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n(8n-7)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo stretchy="false">(</mo> <mn>8</mn> <mi>n</mi> <mo>−</mo> <mn>7</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n(8n-7)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/29d47bf617feb96918b1c32c7a00529b4655255f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.764ex; height:2.843ex;" alt="{\displaystyle n(8n-7)}"></span> </td> <td>0, 1, 18, 51, 100, 165, 246, 343, 456, 585, 730, 891, 1068, 1261, 1470, 1695, 1936, 2193, 2466, 2755, ... </td> <td><a href="//oeis.org/A051870" class="extiw" title="oeis:A051870">A051870</a> </td></tr> <tr> <td>19 </td> <td>십구각수(十九角數, <span style="font-size: smaller;"><a href="/wiki/%EC%98%81%EC%96%B4" title="영어">영어</a>: </span><span lang="en">nonadecagonal number</span>) </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n(17n-15)/2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo stretchy="false">(</mo> <mn>17</mn> <mi>n</mi> <mo>−</mo> <mn>15</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n(17n-15)/2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a390a7ccdd3b89acc1c14c8d39c8dd581801ad7f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.414ex; height:2.843ex;" alt="{\displaystyle n(17n-15)/2}"></span> </td> <td>0, 1, 19, 54, 106, 175, 261, 364, 484, 621, 775, 946, 1134, 1339, 1561, 1800, 2056, 2329, 2619, 2926, ... </td> <td><a href="//oeis.org/A051871" class="extiw" title="oeis:A051871">A051871</a> </td></tr> <tr> <td>20 </td> <td>이십각수(二十角數, <span style="font-size: smaller;"><a href="/wiki/%EC%98%81%EC%96%B4" title="영어">영어</a>: </span><span lang="en">Icosagonal number</span>) </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n(9n-8)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo stretchy="false">(</mo> <mn>9</mn> <mi>n</mi> <mo>−</mo> <mn>8</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n(9n-8)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4abe76d63b715e3920100915cd735568ae56bfea" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.764ex; height:2.843ex;" alt="{\displaystyle n(9n-8)}"></span> </td> <td>0, 1, 20, 57, 112, 185, 276, 385, 512, 657, 820, 1001, 1200, 1417, 1652, 1905, 2176, 2465, 2772, 3097, ... </td> <td><a href="//oeis.org/A051872" class="extiw" title="oeis:A051872">A051872</a> </td></tr> <tr> <td>21 </td> <td>이십일각수(二十一角數, <span style="font-size: smaller;"><a href="/wiki/%EC%98%81%EC%96%B4" title="영어">영어</a>: </span><span lang="en">icosihenagonal number</span>) </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n(19n-17)/2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo stretchy="false">(</mo> <mn>19</mn> <mi>n</mi> <mo>−</mo> <mn>17</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n(19n-17)/2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1d6f0b9d380a4e048c3598d4170ce464eb22a1a0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.414ex; height:2.843ex;" alt="{\displaystyle n(19n-17)/2}"></span> </td> <td>0, 1, 21, 60, 118, 195, 291, 406, 540, 693, 865, 1056, 1266, 1495, 1743, 2010, 2296, 2601, 2925, 3268, ... </td> <td><a href="//oeis.org/A051873" class="extiw" title="oeis:A051873">A051873</a> </td></tr> <tr> <td>22 </td> <td>이십이각수(二十二角數, <span style="font-size: smaller;"><a href="/wiki/%EC%98%81%EC%96%B4" title="영어">영어</a>: </span><span lang="en">icosidigonal number</span>) </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n(10n-9)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo stretchy="false">(</mo> <mn>10</mn> <mi>n</mi> <mo>−</mo> <mn>9</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n(10n-9)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/897981ffcc7fb5022904bbec858437a6263136ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.926ex; height:2.843ex;" alt="{\displaystyle n(10n-9)}"></span> </td> <td>0, 1, 22, 63, 124, 205, 306, 427, 568, 729, 910, 1111, 1332, 1573, 1834, 2115, 2416, 2737, 3078, 3439, ... </td> <td><a href="//oeis.org/A051874" class="extiw" title="oeis:A051874">A051874</a> </td></tr> <tr> <td>23 </td> <td>이십삼각수(二十三角數, <span style="font-size: smaller;"><a href="/wiki/%EC%98%81%EC%96%B4" title="영어">영어</a>: </span><span lang="en">icositrigonal number</span>) </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n(21n-19)/2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo stretchy="false">(</mo> <mn>21</mn> <mi>n</mi> <mo>−</mo> <mn>19</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n(21n-19)/2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/12d50bec6da5846cc07d3e7e8cee3448e580705e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.414ex; height:2.843ex;" alt="{\displaystyle n(21n-19)/2}"></span> </td> <td>0, 1, 23, 66, 130, 215, 321, 448, 596, 765, 955, 1166, 1398, 1651, 1925, 2220, 2536, 2873, 3231, 3610, ... </td> <td><a href="//oeis.org/A051875" class="extiw" title="oeis:A051875">A051875</a> </td></tr> <tr> <td>24 </td> <td>이십사각수(二十四角數, <span style="font-size: smaller;"><a href="/wiki/%EC%98%81%EC%96%B4" title="영어">영어</a>: </span><span lang="en">icositetragonal number</span>) </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n(11n-10)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo stretchy="false">(</mo> <mn>11</mn> <mi>n</mi> <mo>−</mo> <mn>10</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n(11n-10)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0c163eff50be1e809b0f0ba47b146da0ed94881b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.089ex; height:2.843ex;" alt="{\displaystyle n(11n-10)}"></span> </td> <td>0, 1, 24, 69, 136, 225, 336, 469, 624, 801, 1000, 1221, 1464, 1729, 2016, 2325, 2656, 3009, 3384, 3781, ... </td> <td><a href="//oeis.org/A051876" class="extiw" title="oeis:A051876">A051876</a> </td></tr> <tr> <td>25 </td> <td>이십오각수(二十五角數, <span style="font-size: smaller;"><a href="/wiki/%EC%98%81%EC%96%B4" title="영어">영어</a>: </span><span lang="en">icosipentagonal number</span>) </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n(23n-21)/2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo stretchy="false">(</mo> <mn>23</mn> <mi>n</mi> <mo>−</mo> <mn>21</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n(23n-21)/2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6539c7b8312f50059bff9a78c2ee1fa76ddc39f6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.414ex; height:2.843ex;" alt="{\displaystyle n(23n-21)/2}"></span> </td> <td>0, 1, 25, 72, 142, 235, 351, 490, 652, 837, 1045, 1276, 1530, 1807, 2107, 2430, 2776, 3145, 3537, 3952, ... </td> <td><a href="//oeis.org/A255184" class="extiw" title="oeis:A255184">A255184</a> </td></tr> <tr> <td>26 </td> <td>이십육각수(二十六角數, <span style="font-size: smaller;"><a href="/wiki/%EC%98%81%EC%96%B4" title="영어">영어</a>: </span><span lang="en">icosihexagonal number</span>) </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n(12n-11)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo stretchy="false">(</mo> <mn>12</mn> <mi>n</mi> <mo>−</mo> <mn>11</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n(12n-11)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/69b5ea61f1e6e58a114a3feb8f753b6276351ba4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.089ex; height:2.843ex;" alt="{\displaystyle n(12n-11)}"></span> </td> <td>0, 1, 26, 75, 148, 245, 366, 511, 680, 873, 1090, 1331, 1596, 1885, 2198, 2535, 2896, 3281, 3690, 4123, ... </td> <td><a href="//oeis.org/A255185" class="extiw" title="oeis:A255185">A255185</a> </td></tr> <tr> <td>27 </td> <td>이십칠각수(二十七角數, <span style="font-size: smaller;"><a href="/wiki/%EC%98%81%EC%96%B4" title="영어">영어</a>: </span><span lang="en">icosiheptagonal number</span>) </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n(25n-23)/2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo stretchy="false">(</mo> <mn>25</mn> <mi>n</mi> <mo>−</mo> <mn>23</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n(25n-23)/2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec1f31537f83ccb77d964e370557fefa1d7976af" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.414ex; height:2.843ex;" alt="{\displaystyle n(25n-23)/2}"></span> </td> <td>0, 1, 27, 78, 154, 255, 381, 532, 708, 909, 1135, 1386, 1662, 1963, 2289, 2640, 3016, 3417, 3843, 4294, ... </td> <td><a href="//oeis.org/A255186" class="extiw" title="oeis:A255186">A255186</a> </td></tr> <tr> <td>28 </td> <td>이십팔각수(二十八角數, <span style="font-size: smaller;"><a href="/wiki/%EC%98%81%EC%96%B4" title="영어">영어</a>: </span><span lang="en">icosioctagonal number</span>) </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n(13n-12)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo stretchy="false">(</mo> <mn>13</mn> <mi>n</mi> <mo>−</mo> <mn>12</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n(13n-12)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/52792c9901a046a80e28e30465d6d9dbe3e942cf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.089ex; height:2.843ex;" alt="{\displaystyle n(13n-12)}"></span> </td> <td>0, 1, 28, 81, 160, 265, 396, 553, 736, 945, 1180, 1441, 1728, 2041, 2380, 2745, 3136, 3553, 3996, 4465, ... </td> <td><a href="//oeis.org/A161935" class="extiw" title="oeis:A161935">A161935</a> </td></tr> <tr> <td>29 </td> <td>이십구각수(二十九角數, <span style="font-size: smaller;"><a href="/wiki/%EC%98%81%EC%96%B4" title="영어">영어</a>: </span><span lang="en">icosinonagonal number</span>) </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n(27n-25)/2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo stretchy="false">(</mo> <mn>27</mn> <mi>n</mi> <mo>−</mo> <mn>25</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n(27n-25)/2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e584a8c929cd29010a91f03385fdb87b0ab58ad7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.414ex; height:2.843ex;" alt="{\displaystyle n(27n-25)/2}"></span> </td> <td>0, 1, 29, 84, 166, 275, 411, 574, 764, 981, 1225, 1496, 1794, 2119, 2471, 2850, 3256, 3689, 4149, 4636, ... </td> <td><a href="//oeis.org/A255187" class="extiw" title="oeis:A255187">A255187</a> </td></tr> <tr> <td>30 </td> <td>삼십각수(三十角數, <span style="font-size: smaller;"><a href="/wiki/%EC%98%81%EC%96%B4" title="영어">영어</a>: </span><span lang="en">triacontagonal number</span>) </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n(14n-13)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo stretchy="false">(</mo> <mn>14</mn> <mi>n</mi> <mo>−</mo> <mn>13</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n(14n-13)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e8acef716d3c126646d08de406b71c8877816ea4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.089ex; height:2.843ex;" alt="{\displaystyle n(14n-13)}"></span> </td> <td>0, 1, 30, 87, 172, 285, 426, 595, 792, 1017, 1270, 1551, 1860, 2197, 2562, 2955, 3376, 3825, 4302, 4807, ... </td> <td><a href="//oeis.org/A254474" class="extiw" title="oeis:A254474">A254474</a> </td></tr></tbody></table> <div class="mw-heading mw-heading4"><h4 id="중심있는_평면도형수"><span id=".EC.A4.91.EC.8B.AC.EC.9E.88.EB.8A.94_.ED.8F.89.EB.A9.B4.EB.8F.84.ED.98.95.EC.88.98"></span>중심있는 평면도형수</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EB%8B%A4%EA%B0%81%EC%88%98&action=edit&section=8" title="부분 편집: 중심있는 평면도형수"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable"> <tbody><tr> <th><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07d98bb302f3856cbabc47b2b9016692e3f7bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.04ex; height:1.676ex;" alt="{\displaystyle m}"></span> </th> <th>명칭 </th> <th><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \operatorname {Pol} (m;n)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Pol</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>m</mi> <mo>;</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \operatorname {Pol} (m;n)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/53a35a2eebf23d8e21e98120da96139f10a9a014" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.67ex; height:2.843ex;" alt="{\displaystyle \operatorname {Pol} (m;n)}"></span> </th> <th>처음 20항 (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 0\leq n\leq 19}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>0</mn> <mo>≤</mo> <mi>n</mi> <mo>≤</mo> <mn>19</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 0\leq n\leq 19}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/96b669c6902e194956b5b019ab0f561518b1b733" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:11.079ex; height:2.343ex;" alt="{\displaystyle 0\leq n\leq 19}"></span>) </th> <th>OEIS </th></tr> <tr> <td>3 </td> <td>중심있는 삼각수 (centered triangular number) </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {3n(n-1)+2}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>3</mn> <mi>n</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>+</mo> <mn>2</mn> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {3n(n-1)+2}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9314fc822e41ab5a6b67c75a7819ff1fb220a81e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:14.603ex; height:5.676ex;" alt="{\displaystyle {\frac {3n(n-1)+2}{2}}}"></span> </td> <td>1, 1, 4, 10, 19, 31, 46, 64, 85, 109, 136, 166, 199, 235, 274, 316, 361, 409, 460, 514, … </td> <td><a href="//oeis.org/A005448" class="extiw" title="oeis:A005448">A005448</a> </td></tr> <tr> <td>4 </td> <td>중심있는 사각수 (centered square number) </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2n(n-1)+1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mi>n</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>+</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2n(n-1)+1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d0ed6f33d7099fb27fc9640bf9b09a533129de71" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.767ex; height:2.843ex;" alt="{\displaystyle 2n(n-1)+1}"></span> </td> <td>1, 1, 5, 13, 25, 41, 61, 85, 113, 145, 181, 221, 265, 313, 365, 421, 481, 545, 613, 685, … </td> <td><a href="//oeis.org/A001844" class="extiw" title="oeis:A001844">A001844</a> </td></tr> <tr> <td>5 </td> <td>중심있는 오각수 (centered pentagonal number) </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {5n(n-1)+2}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>5</mn> <mi>n</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>+</mo> <mn>2</mn> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {5n(n-1)+2}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/be6b1333e3a7e762ec11127f9fc269706bddbeca" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:14.603ex; height:5.676ex;" alt="{\displaystyle {\frac {5n(n-1)+2}{2}}}"></span> </td> <td>1, 1, 6, 16, 31, 51, 76, 106, 141, 181, 226, 276, 331, 391, 456, 526, 601, 681, 766, 856, … </td> <td><a href="//oeis.org/A005891" class="extiw" title="oeis:A005891">A005891</a> </td></tr> <tr> <td>6 </td> <td>중심있는 육각수 (centered hexagonal number) </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 3n(n-1)+1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>3</mn> <mi>n</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>+</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 3n(n-1)+1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d0611298b22ddbc408a5c9236452b43076e8b828" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.767ex; height:2.843ex;" alt="{\displaystyle 3n(n-1)+1}"></span> </td> <td>1, 1, 7, 19, 37, 61, 91, 127, 169, 217, 271, 331, 397, 469, 547, 631, 721, 817, 919, 1027, … </td> <td><a href="//oeis.org/A003215" class="extiw" title="oeis:A003215">A003215</a> </td></tr> <tr> <td>7 </td> <td>중심있는 칠각수 (centered heptagonal numbers) </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {7n(n-1)+1}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>7</mn> <mi>n</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>+</mo> <mn>1</mn> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {7n(n-1)+1}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b634e886922d6f3470cf3f3d55ee9b4c6d655fe7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:14.603ex; height:5.676ex;" alt="{\displaystyle {\frac {7n(n-1)+1}{2}}}"></span> </td> <td>1, 1, 8, 22, 43, 71, 106, 148, 197, 253, 316, 386, 463, 547, 638, 736, 841, 953, 1072, 1198, … </td> <td><a href="//oeis.org/A069099" class="extiw" title="oeis:A069099">A069099</a> </td></tr> <tr> <td>8 </td> <td>중심있는 팔각수 (centered octagonal numbers) </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (2n-1)^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mn>2</mn> <mi>n</mi> <mo>−</mo> <mn>1</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (2n-1)^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c50ef48bbb8fce9645a0d62264b1214175b669af" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.424ex; height:3.176ex;" alt="{\displaystyle (2n-1)^{2}}"></span> </td> <td>1, 1, 9, 25, 49, 81, 121, 169, 225, 289, 361, 441, 529, 625, 729, 841, 961, 1089, 1225, 1369, … </td> <td><a href="//oeis.org/A016754" class="extiw" title="oeis:A016754">A016754</a> </td></tr> <tr> <td>9 </td> <td>중심있는 구각수 (centered nonagonal number) </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {(3n-2)(3n-1)}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mn>3</mn> <mi>n</mi> <mo>−</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mn>3</mn> <mi>n</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {(3n-2)(3n-1)}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/30af7fc89857e51f4bc2c9880cdc7c149c8929dc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:17.575ex; height:5.676ex;" alt="{\displaystyle {\frac {(3n-2)(3n-1)}{2}}}"></span> </td> <td>1, 1, 10, 28, 55, 91, 136, 190, 253, 325, 406, 496, 595, 703, 820, 946, 1081, 1225, 1378, 1540, … </td> <td><a href="//oeis.org/A060544" class="extiw" title="oeis:A060544">A060544</a> </td></tr> <tr> <td>10 </td> <td>중심있는 십각수 (centered decagonal number) </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 5n(n-1)+1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>5</mn> <mi>n</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>+</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 5n(n-1)+1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7e27a3b171d16c802d1f2237518201cf54310a60" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.767ex; height:2.843ex;" alt="{\displaystyle 5n(n-1)+1}"></span> </td> <td>1, 1, 11, 31, 61, 101, 151, 211, 281, 361, 451, 551, 661, 781, 911, 1051, 1201, 1361, 1531, 1711, … </td> <td><a href="//oeis.org/A062786" class="extiw" title="oeis:A062786">A062786</a> </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="입체도형수"><span id=".EC.9E.85.EC.B2.B4.EB.8F.84.ED.98.95.EC.88.98"></span>입체도형수</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EB%8B%A4%EA%B0%81%EC%88%98&action=edit&section=9" title="부분 편집: 입체도형수"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="다면체수"><span id=".EB.8B.A4.EB.A9.B4.EC.B2.B4.EC.88.98"></span>다면체수</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EB%8B%A4%EA%B0%81%EC%88%98&action=edit&section=10" title="부분 편집: 다면체수"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable"> <tbody><tr> <th>명칭 </th> <th><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \operatorname {Pol} (n)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Pol</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \operatorname {Pol} (n)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a1579b1128fa1310a31d9b537557493c7129a03" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.596ex; height:2.843ex;" alt="{\displaystyle \operatorname {Pol} (n)}"></span> </th> <th>처음 20항 (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 0\leq n\leq 19}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>0</mn> <mo>≤</mo> <mi>n</mi> <mo>≤</mo> <mn>19</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 0\leq n\leq 19}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/96b669c6902e194956b5b019ab0f561518b1b733" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:11.079ex; height:2.343ex;" alt="{\displaystyle 0\leq n\leq 19}"></span>) </th> <th>OEIS </th></tr> <tr> <td><a href="/wiki/%EC%82%AC%EB%A9%B4%EC%B2%B4%EC%88%98" title="사면체수">사면체수</a>(tetrahedral number) / 삼각뿔수(triangular pyramidal number)</td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {n(n+1)(n+2)}{6}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>n</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>n</mi> <mo>+</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> <mn>6</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {n(n+1)(n+2)}{6}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b668a2837aa464156f1b2c5aa84a448b147593c5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:16.645ex; height:5.676ex;" alt="{\displaystyle {\frac {n(n+1)(n+2)}{6}}}"></span></td> <td>0, 1, 4, 10, 20, 35, 56, 84, 120, 165, 220, 286, 364, 455, 560, 680, 816, 969, 1140, 1330, …</td> <td><a href="//oeis.org/A000292" class="extiw" title="oeis:A000292">A000292</a> </td></tr> <tr> <td>육면체수 / <a href="/wiki/%EC%84%B8%EC%A0%9C%EA%B3%B1%EC%88%98" title="세제곱수">입방수</a>(cubic number)</td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n^{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n^{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3e9d1a52e455a7a5272a345b2697e35f1579b681" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.449ex; height:2.676ex;" alt="{\displaystyle n^{3}}"></span></td> <td>0, 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, 1728, 2197, 2744, 3375, 4096, 4913, 5832, 6859, …</td> <td><a href="//oeis.org/A000578" class="extiw" title="oeis:A000578">A000578</a> </td></tr> <tr> <td><a href="/wiki/%ED%8C%94%EB%A9%B4%EC%B2%B4%EC%88%98" title="팔면체수">팔면체수</a>(octahedral number)</td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {n(2n^{2}+1)}{3}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>n</mi> <mo stretchy="false">(</mo> <mn>2</mn> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> <mn>3</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {n(2n^{2}+1)}{3}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/40f06ad3c38d27c3543c3f25e3efc66f9c9c393f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:11.654ex; height:5.843ex;" alt="{\displaystyle {\frac {n(2n^{2}+1)}{3}}}"></span></td> <td>0, 1, 6, 19, 44, 85, 146, 231, 344, 489, 670, 891, 1156, 1469, 1834, 2255, 2736, 3281, 3894, 4579, …</td> <td><a href="//oeis.org/A005900" class="extiw" title="oeis:A005900">A005900</a> </td></tr> <tr> <td>십이면체수(dodecahedral number)</td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {n(3n-1)(3n-2) \over 2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>n</mi> <mo stretchy="false">(</mo> <mn>3</mn> <mi>n</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mn>3</mn> <mi>n</mi> <mo>−</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {n(3n-1)(3n-2) \over 2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/acd68e068b25acdc21afd82cdec2b6b3214d5141" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:18.969ex; height:5.676ex;" alt="{\displaystyle {n(3n-1)(3n-2) \over 2}}"></span></td> <td>0, 1, 20, 84, 220, 455, 816, 1330, 2024, 2925, 4060, 5456, 7140, 9139, 11480, 14190, 17296, 20825, 24804, 29260, …</td> <td><a href="//oeis.org/A006566" class="extiw" title="oeis:A006566">A006566</a> </td></tr> <tr> <td>이십면체수(icosahedral number)</td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {n(5n^{2}-5n+2) \over 2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>n</mi> <mo stretchy="false">(</mo> <mn>5</mn> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>5</mn> <mi>n</mi> <mo>+</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {n(5n^{2}-5n+2) \over 2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fb2acf163539418f1afeae275774c75dc85c4e90" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:17.052ex; height:5.843ex;" alt="{\displaystyle {n(5n^{2}-5n+2) \over 2}}"></span></td> <td>0, 1, 12, 48, 124, 255, 456, 742, 1128, 1629, 2260, 3036, 3972, 5083, 6384, 7890, 9616, 11577, 13788, 16264, …</td> <td><a href="//oeis.org/A006564" class="extiw" title="oeis:A006564">A006564</a> </td></tr> <tr> <td><a href="/wiki/%EC%82%AC%EA%B0%81%EB%BF%94%EC%88%98" title="사각뿔수">사각뿔수</a>(square pyramidal number)</td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {1}{3}}n^{3}+{\frac {1}{2}}n^{2}+{\frac {1}{6}}n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>3</mn> </mfrac> </mrow> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>6</mn> </mfrac> </mrow> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{3}}n^{3}+{\frac {1}{2}}n^{2}+{\frac {1}{6}}n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bfa7600204372b700eb7b383b4ed4c7aee520581" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:17.969ex; height:5.176ex;" alt="{\displaystyle {\frac {1}{3}}n^{3}+{\frac {1}{2}}n^{2}+{\frac {1}{6}}n}"></span></td> <td>0, 1, 5, 14, 30, 55, 91, 140, 204, 285, 385, 506, 650, 819, 1015, 1240, 1496, 1785, 2109, 2470, …</td> <td><a href="//oeis.org/A000330" class="extiw" title="oeis:A000330">A000330</a> </td></tr> <tr> <td>오각뿔수(pentagonal pyramidal number)</td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {n^{2}(n+1)}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {n^{2}(n+1)}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/435fff983d9fe0d26aa0c0b95be32b7c8ae00b6c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:10.492ex; height:5.843ex;" alt="{\displaystyle {\frac {n^{2}(n+1)}{2}}}"></span></td> <td>0, 1, 6, 18, 40, 75, 126, 196, 288, 405, 550, 726, 936, 1183, 1470, 1800, 2176, 2601, 3078, 3610, …</td> <td><a href="//oeis.org/A002411" class="extiw" title="oeis:A002411">A002411</a> </td></tr> <tr> <td>육각뿔수(hexagonal pyramidal number)</td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {n(n+1)(4n-1)}{6}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>n</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mn>4</mn> <mi>n</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> <mn>6</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {n(n+1)(4n-1)}{6}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8980ba2c2dbf86c4e44e10a5de13da02ffe36a3f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:17.807ex; height:5.676ex;" alt="{\displaystyle {\frac {n(n+1)(4n-1)}{6}}}"></span></td> <td>0, 1, 7, 22, 50, 95, 161, 252, 372, 525, 715, 946, 1222, 1547, 1925, 2360, 2856, 3417, 4047, 4750, …</td> <td><a href="//oeis.org/A002412" class="extiw" title="oeis:A002412">A002412</a> </td></tr> <tr> <td>칠각뿔수(heptagonal pyramidal number)</td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {n(n+1)(5n-2)}{6}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>n</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mn>5</mn> <mi>n</mi> <mo>−</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> <mn>6</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {n(n+1)(5n-2)}{6}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c5f97cb9875c80d858166a7a47c4d93a300b8659" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:17.807ex; height:5.676ex;" alt="{\displaystyle {\frac {n(n+1)(5n-2)}{6}}}"></span></td> <td>0, 1, 8, 26, 60, 115, 196, 308, 456, 645, 880, 1166, 1508, 1911, 2380, 2920, 3536, 4233, 5016, 5890, …</td> <td><a href="//oeis.org/A002413" class="extiw" title="oeis:A002413">A002413</a> </td></tr></tbody></table> <div class="mw-heading mw-heading4"><h4 id="다포체수"><span id=".EB.8B.A4.ED.8F.AC.EC.B2.B4.EC.88.98"></span>다포체수</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EB%8B%A4%EA%B0%81%EC%88%98&action=edit&section=11" title="부분 편집: 다포체수"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable"> <tbody><tr> <th>명칭 </th> <th><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \operatorname {Pol} (n)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Pol</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \operatorname {Pol} (n)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a1579b1128fa1310a31d9b537557493c7129a03" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.596ex; height:2.843ex;" alt="{\displaystyle \operatorname {Pol} (n)}"></span> </th> <th>처음 20항 (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 0\leq n\leq 19}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>0</mn> <mo>≤</mo> <mi>n</mi> <mo>≤</mo> <mn>19</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 0\leq n\leq 19}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/96b669c6902e194956b5b019ab0f561518b1b733" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:11.079ex; height:2.343ex;" alt="{\displaystyle 0\leq n\leq 19}"></span>) </th> <th>OEIS </th></tr> <tr> <td>오포체수(pentatope number)</td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {n(n+1)(n+2)(n+3)}{24}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>n</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>n</mi> <mo>+</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>n</mi> <mo>+</mo> <mn>3</mn> <mo stretchy="false">)</mo> </mrow> <mn>24</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {n(n+1)(n+2)(n+3)}{24}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3776ae2056fe63ab196c20b5f30f39492a09fb56" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:23.851ex; height:5.676ex;" alt="{\displaystyle {\frac {n(n+1)(n+2)(n+3)}{24}}}"></span></td> <td>0, 0, 0, 0, 1, 5, 15, 35, 70, 126, 210, 330, 495, 715, 1001, 1365, 1820, 2380, 3060, 3876, …</td> <td><a href="//oeis.org/A000332" class="extiw" title="oeis:A000332">A000332</a> </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="역사"><span id=".EC.97.AD.EC.82.AC"></span>역사</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EB%8B%A4%EA%B0%81%EC%88%98&action=edit&section=12" title="부분 편집: 역사"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>일반적인 다각수는 힙시클레스(<span style="font-size: smaller;"><a href="/wiki/%EA%B7%B8%EB%A6%AC%EC%8A%A4%EC%96%B4" title="그리스어">그리스어</a>: </span><span lang="grc-gre">Ὑψικλῆς</span>)가 기원전 2세기에 처음 정의하였다. </p> <div class="mw-heading mw-heading2"><h2 id="같이_보기"><span id=".EA.B0.99.EC.9D.B4_.EB.B3.B4.EA.B8.B0"></span>같이 보기</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EB%8B%A4%EA%B0%81%EC%88%98&action=edit&section=13" title="부분 편집: 같이 보기"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/%ED%8E%98%EB%A5%B4%EB%A7%88_%EB%8B%A4%EA%B0%81%EC%88%98_%EC%A0%95%EB%A6%AC" title="페르마 다각수 정리">페르마 다각수 정리</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="외부_링크"><span id=".EC.99.B8.EB.B6.80_.EB.A7.81.ED.81.AC"></span>외부 링크</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EB%8B%A4%EA%B0%81%EC%88%98&action=edit&section=14" title="부분 편집: 외부 링크"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><cite class="citation web"><a rel="nofollow" class="external text" href="https://encyclopediaofmath.org/wiki/Polygonal_number">“Polygonal number”</a>. 《Encyclopedia of Mathematics》 (영어). Springer-Verlag. 2001. <a href="/wiki/%EA%B5%AD%EC%A0%9C_%ED%91%9C%EC%A4%80_%EB%8F%84%EC%84%9C_%EB%B2%88%ED%98%B8" class="mw-redirect" title="국제 표준 도서 번호">ISBN</a> <a href="/wiki/%ED%8A%B9%EC%88%98:%EC%B1%85%EC%B0%BE%EA%B8%B0/978-1-55608-010-4" title="특수:책찾기/978-1-55608-010-4"><bdi>978-1-55608-010-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Encyclopedia+of+Mathematics&rft.atitle=Polygonal+number&rft.date=2001&rft.isbn=978-1-55608-010-4&rft_id=https%3A%2F%2Fencyclopediaofmath.org%2Fwiki%2FPolygonal_number&rfr_id=info%3Asid%2Fko.wikipedia.org%3A%EB%8B%A4%EA%B0%81%EC%88%98" class="Z3988"><span style="display:none;"> </span></span></li> <li><cite class="citation web">Weisstein, Eric Wolfgang. <a rel="nofollow" class="external text" href="https://mathworld.wolfram.com/PolygonalNumber.html">“Polygonal number”</a>. 《<a href="/wiki/%EB%A7%A4%EC%8A%A4%EC%9B%94%EB%93%9C" title="매스월드">Wolfram MathWorld</a>》 (영어). Wolfram Research.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Wolfram+MathWorld&rft.atitle=Polygonal+number&rft.aulast=Weisstein&rft.aufirst=Eric+Wolfgang&rft_id=https%3A%2F%2Fmathworld.wolfram.com%2FPolygonalNumber.html&rfr_id=info%3Asid%2Fko.wikipedia.org%3A%EB%8B%A4%EA%B0%81%EC%88%98" class="Z3988"><span style="display:none;"> </span></span></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r36480591">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol 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