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href="/w/index.php?title=Posebno:Prijava&returnto=Fibonaccijevo+%C5%A1tevilo" title="Prijava je zaželena, vendar ni obvezna [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Prijava</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"> Strani za neprijavljene urejevalce <a href="/wiki/Pomo%C4%8D:Uvod" aria-label="Več o urejanju"><span>več o tem</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/Posebno:MojiPrispevki" title="Seznam urejanj s tega IP-naslova [y]" accesskey="y"><span>Prispevki</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Posebno:MojPogovor" title="Pogovor o urejanjih s tega IP-naslova [n]" accesskey="n"><span>Pogovorna stran</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="Projekt"> <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="Vsebina" 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">Vsebina</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">prestavi v stransko letvico</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">skrij</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">Uvod</div> </a> </li> <li id="toc-Enačba" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Enačba"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Enačba</span> </div> </a> <ul id="toc-Enačba-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Računanje_Fibonaccijevih_števil" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Računanje_Fibonaccijevih_števil"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Računanje Fibonaccijevih števil</span> </div> </a> <ul id="toc-Računanje_Fibonaccijevih_števil-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Uporabe" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Uporabe"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Uporabe</span> </div> </a> <ul id="toc-Uporabe-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Posplošitve" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Posplošitve"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Posplošitve</span> </div> </a> <ul id="toc-Posplošitve-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Algoritem" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Algoritem"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Algoritem</span> </div> </a> <ul id="toc-Algoritem-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Fibonaccijeva_števila_v_naravi" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Fibonaccijeva_števila_v_naravi"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Fibonaccijeva števila v naravi</span> </div> </a> <ul id="toc-Fibonaccijeva_števila_v_naravi-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Fibonaccijeva_števila_v_leposlovju" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Fibonaccijeva_števila_v_leposlovju"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Fibonaccijeva števila v leposlovju</span> </div> </a> <ul id="toc-Fibonaccijeva_števila_v_leposlovju-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Glej_tudi" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Glej_tudi"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Glej tudi</span> </div> </a> <ul id="toc-Glej_tudi-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Sklici" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Sklici"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Sklici</span> </div> </a> <ul id="toc-Sklici-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Viri" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Viri"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Viri</span> </div> </a> <ul id="toc-Viri-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="Vsebina" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <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="Vklopi kazalo vsebine" > <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">Vklopi kazalo vsebine</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">Fibonaccijevo število</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="P9jdi na članek v drugem jeziku. Na voljo v 63 jezikih." > <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-63" 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">63 jezikov</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar badge-Q70894304 mw-list-item" title=""><a href="https://ar.wikipedia.org/wiki/%D8%B9%D8%AF%D8%AF_%D9%81%D9%8A%D8%A8%D9%88%D9%86%D8%A7%D8%AA%D8%B4%D9%8A" title="عدد فيبوناتشي – arabščina" lang="ar" hreflang="ar" data-title="عدد فيبوناتشي" data-language-autonym="العربية" data-language-local-name="arabščina" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Fibona%C3%A7%C3%A7i_%C9%99d%C9%99dl%C9%99ri" title="Fibonaççi ədədləri – azerbajdžanščina" lang="az" hreflang="az" data-title="Fibonaççi ədədləri" data-language-autonym="Azərbaycanca" data-language-local-name="azerbajdžanščina" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%A4%D0%B8%D0%B1%D0%BE%D0%BD%D0%B0%D1%87%D1%87%D0%B8_%D2%BB%D0%B0%D0%BD%D0%B4%D0%B0%D1%80%D1%8B" title="Фибоначчи һандары – baškirščina" lang="ba" hreflang="ba" data-title="Фибоначчи һандары" data-language-autonym="Башҡортса" data-language-local-name="baškirščina" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9B%D1%96%D0%BA%D1%96_%D0%A4%D1%96%D0%B1%D0%B0%D0%BD%D0%B0%D1%87%D1%8B" title="Лікі Фібаначы – beloruščina" lang="be" hreflang="be" data-title="Лікі Фібаначы" data-language-autonym="Беларуская" data-language-local-name="beloruščina" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A7%D0%B8%D1%81%D0%BB%D0%B0_%D0%BD%D0%B0_%D0%A4%D0%B8%D0%B1%D0%BE%D0%BD%D0%B0%D1%87%D0%B8" title="Числа на Фибоначи – bolgarščina" lang="bg" hreflang="bg" data-title="Числа на Фибоначи" data-language-autonym="Български" data-language-local-name="bolgarščina" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Fibonaccijev_broj" title="Fibonaccijev broj – bosanščina" lang="bs" hreflang="bs" data-title="Fibonaccijev broj" data-language-autonym="Bosanski" data-language-local-name="bosanščina" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Nombre_de_Fibonacci" title="Nombre de Fibonacci – katalonščina" lang="ca" hreflang="ca" data-title="Nombre de Fibonacci" data-language-autonym="Català" data-language-local-name="katalonščina" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%DA%98%D9%85%D8%A7%D8%B1%DB%95%DB%8C_%D9%81%DB%8C%D8%A8%DB%86%D9%86%D8%A7%DA%86%DB%8C" title="ژمارەی فیبۆناچی – osrednja kurdščina" lang="ckb" hreflang="ckb" data-title="ژمارەی فیبۆناچی" data-language-autonym="کوردی" data-language-local-name="osrednja kurdščina" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cu mw-list-item"><a href="https://cu.wikipedia.org/wiki/%D0%A4%D1%97%D0%B2%D0%BE%D0%BD%D0%B0%D0%BA%D1%97%D0%B8%D0%BD%D0%BE%D0%B2%D0%B8_%D1%87%D0%B8%D1%81%D0%BC%D1%94%D0%BD%D0%B0" title="Фївонакїинови чисмєна – stara cerkvena slovanščina" lang="cu" hreflang="cu" data-title="Фївонакїинови чисмєна" data-language-autonym="Словѣньскъ / ⰔⰎⰑⰂⰡⰐⰠⰔⰍⰟ" data-language-local-name="stara cerkvena slovanščina" class="interlanguage-link-target"><span>Словѣньскъ / ⰔⰎⰑⰂⰡⰐⰠⰔⰍⰟ</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A4%D0%B8%D0%B1%D0%BE%D0%BD%D0%B0%D1%87%D1%87%D0%B8_%D1%85%D0%B8%D1%81%D0%B5%D0%BF%C4%95" title="Фибоначчи хисепĕ – čuvaščina" lang="cv" hreflang="cv" data-title="Фибоначчи хисепĕ" data-language-autonym="Чӑвашла" data-language-local-name="čuvaščina" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Rhif_Fibonacci" title="Rhif Fibonacci – valižanščina" lang="cy" hreflang="cy" data-title="Rhif Fibonacci" data-language-autonym="Cymraeg" data-language-local-name="valižanščina" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Fibonacci-tal" title="Fibonacci-tal – danščina" lang="da" hreflang="da" data-title="Fibonacci-tal" data-language-autonym="Dansk" data-language-local-name="danščina" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de badge-Q70894304 mw-list-item" title=""><a href="https://de.wikipedia.org/wiki/Fibonaccizahl" title="Fibonaccizahl – nemščina" lang="de" hreflang="de" data-title="Fibonaccizahl" data-language-autonym="Deutsch" data-language-local-name="nemščina" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en badge-Q70893996 mw-list-item" title=""><a href="https://en.wikipedia.org/wiki/Fibonacci_number" title="Fibonacci number – angleščina" lang="en" hreflang="en" data-title="Fibonacci number" data-language-autonym="English" data-language-local-name="angleščina" 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/Fibona%C4%89i-nombro" title="Fibonaĉi-nombro – esperanto" lang="eo" hreflang="eo" data-title="Fibonaĉi-nombro" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es badge-Q70894304 mw-list-item" title=""><a href="https://es.wikipedia.org/wiki/N%C3%BAmero_de_Fibonacci" title="Número de Fibonacci – španščina" lang="es" hreflang="es" data-title="Número de Fibonacci" data-language-autonym="Español" data-language-local-name="španščina" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Fibonacci_jada" title="Fibonacci jada – estonščina" lang="et" hreflang="et" data-title="Fibonacci jada" data-language-autonym="Eesti" data-language-local-name="estonščina" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Fibonacciren_zenbakiak" title="Fibonacciren zenbakiak – baskovščina" lang="eu" hreflang="eu" data-title="Fibonacciren zenbakiak" data-language-autonym="Euskara" data-language-local-name="baskovščina" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A7%D8%B9%D8%AF%D8%A7%D8%AF_%D9%81%DB%8C%D8%A8%D9%88%D9%86%D8%A7%DA%86%DB%8C" title="اعداد فیبوناچی – perzijščina" lang="fa" hreflang="fa" data-title="اعداد فیبوناچی" data-language-autonym="فارسی" data-language-local-name="perzijščina" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fiu-vro mw-list-item"><a href="https://fiu-vro.wikipedia.org/wiki/Fibonacci_arv" title="Fibonacci arv – Võro" lang="vro" hreflang="vro" data-title="Fibonacci arv" data-language-autonym="Võro" data-language-local-name="Võro" class="interlanguage-link-target"><span>Võro</span></a></li><li class="interlanguage-link interwiki-fr badge-Q70894304 mw-list-item" title=""><a href="https://fr.wikipedia.org/wiki/Nombre_de_Fibonacci" title="Nombre de Fibonacci – francoščina" lang="fr" hreflang="fr" data-title="Nombre de Fibonacci" data-language-autonym="Français" data-language-local-name="francoščina" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%AB%E0%AA%BF%E0%AA%AC%E0%AB%8B%E0%AA%A8%E0%AA%BE%E0%AA%95%E0%AA%BF" title="ફિબોનાકિ – gudžaratščina" lang="gu" hreflang="gu" data-title="ફિબોનાકિ" data-language-autonym="ગુજરાતી" data-language-local-name="gudžaratščina" class="interlanguage-link-target"><span>ગુજરાતી</span></a></li><li class="interlanguage-link interwiki-he badge-Q70893996 mw-list-item" title=""><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%A1%D7%A4%D7%A8_%D7%A4%D7%99%D7%91%D7%95%D7%A0%D7%90%D7%A6%27%D7%99" title="מספר פיבונאצ'י – hebrejščina" lang="he" hreflang="he" data-title="מספר פיבונאצ'י" data-language-autonym="עברית" data-language-local-name="hebrejščina" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B9%E0%A5%87%E0%A4%AE%E0%A4%9A%E0%A4%A8%E0%A5%8D%E0%A4%A6%E0%A5%8D%E0%A4%B0_%E0%A4%B6%E0%A5%8D%E0%A4%B0%E0%A5%87%E0%A4%A3%E0%A5%80" title="हेमचन्द्र श्रेणी – hindijščina" lang="hi" hreflang="hi" data-title="हेमचन्द्र श्रेणी" data-language-autonym="हिन्दी" data-language-local-name="hindijščina" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Fibonaccijev_broj" title="Fibonaccijev broj – hrvaščina" lang="hr" hreflang="hr" data-title="Fibonaccijev broj" data-language-autonym="Hrvatski" data-language-local-name="hrvaščina" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Fibonacci-sz%C3%A1mok" title="Fibonacci-számok – madžarščina" lang="hu" hreflang="hu" data-title="Fibonacci-számok" data-language-autonym="Magyar" data-language-local-name="madžarščina" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy badge-Q70893996 mw-list-item" title=""><a href="https://hy.wikipedia.org/wiki/%D5%96%D5%AB%D5%A2%D5%B8%D5%B6%D5%A1%D5%B9%D5%AB%D5%AB_%D5%A9%D5%BE%D5%A5%D6%80" title="Ֆիբոնաչիի թվեր – armenščina" lang="hy" hreflang="hy" data-title="Ֆիբոնաչիի թվեր" data-language-autonym="Հայերեն" data-language-local-name="armenščina" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hyw mw-list-item"><a href="https://hyw.wikipedia.org/wiki/%D5%96%D5%AB%D5%BA%D5%B8%D5%B6%D5%A1%D5%B9%D5%B9%D5%AB%D5%AB_%D5%A9%D5%AB%D6%82" title="Ֆիպոնաչչիի թիւ – Western Armenian" lang="hyw" hreflang="hyw" data-title="Ֆիպոնաչչիի թիւ" data-language-autonym="Արեւմտահայերէն" data-language-local-name="Western Armenian" class="interlanguage-link-target"><span>Արեւմտահայերէն</span></a></li><li class="interlanguage-link interwiki-id badge-Q70893996 mw-list-item" title=""><a href="https://id.wikipedia.org/wiki/Bilangan_Fibonacci" title="Bilangan Fibonacci – indonezijščina" lang="id" hreflang="id" data-title="Bilangan Fibonacci" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonezijščina" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Fibonacci-runan" title="Fibonacci-runan – islandščina" lang="is" hreflang="is" data-title="Fibonacci-runan" data-language-autonym="Íslenska" data-language-local-name="islandščina" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it badge-Q70894304 mw-list-item" title=""><a href="https://it.wikipedia.org/wiki/Numero_di_Fibonacci" title="Numero di Fibonacci – italijanščina" lang="it" hreflang="it" data-title="Numero di Fibonacci" data-language-autonym="Italiano" data-language-local-name="italijanščina" 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/%E3%83%95%E3%82%A3%E3%83%9C%E3%83%8A%E3%83%83%E3%83%81%E6%95%B0" title="フィボナッチ数 – japonščina" lang="ja" hreflang="ja" data-title="フィボナッチ数" data-language-autonym="日本語" data-language-local-name="japonščina" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-kaa mw-list-item"><a href="https://kaa.wikipedia.org/wiki/Fibonachchi_sanlar%C4%B1" title="Fibonachchi sanları – karakalpaščina" lang="kaa" hreflang="kaa" data-title="Fibonachchi sanları" data-language-autonym="Qaraqalpaqsha" data-language-local-name="karakalpaščina" class="interlanguage-link-target"><span>Qaraqalpaqsha</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A4%D0%B8%D0%B1%D0%BE%D0%BD%D0%B0%D1%87%D1%87%D0%B8_%D1%81%D0%B0%D0%BD%D0%B4%D0%B0%D1%80%D1%8B" title="Фибоначчи сандары – kazaščina" lang="kk" hreflang="kk" data-title="Фибоначчи сандары" data-language-autonym="Қазақша" data-language-local-name="kazaščina" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%94%BC%EB%B3%B4%EB%82%98%EC%B9%98_%EC%88%98" title="피보나치 수 – korejščina" lang="ko" hreflang="ko" data-title="피보나치 수" data-language-autonym="한국어" data-language-local-name="korejščina" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Numeri_Fibonacciani" title="Numeri Fibonacciani – latinščina" lang="la" hreflang="la" data-title="Numeri Fibonacciani" data-language-autonym="Latina" data-language-local-name="latinščina" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Fibona%C4%8Di_skait%C4%BCi" title="Fibonači skaitļi – latvijščina" lang="lv" hreflang="lv" data-title="Fibonači skaitļi" data-language-autonym="Latviešu" data-language-local-name="latvijščina" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A4%D0%B8%D0%B1%D0%BE%D0%BD%D0%B0%D1%87%D0%B8%D0%B5%D0%B2%D0%B0_%D0%BD%D0%B8%D0%B7%D0%B0" title="Фибоначиева низа – makedonščina" lang="mk" hreflang="mk" data-title="Фибоначиева низа" data-language-autonym="Македонски" data-language-local-name="makedonščina" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%AB%E0%B4%BF%E0%B4%AC%E0%B4%A8%E0%B4%BE%E0%B4%9A%E0%B5%8D%E0%B4%9A%E0%B4%BF_%E0%B4%B6%E0%B5%8D%E0%B4%B0%E0%B5%87%E0%B4%A3%E0%B4%BF" title="ഫിബനാച്ചി ശ്രേണി – malajalamščina" lang="ml" hreflang="ml" data-title="ഫിബനാച്ചി ശ്രേണി" data-language-autonym="മലയാളം" data-language-local-name="malajalamščina" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%A4%D0%B8%D0%B1%D0%BE%D0%BD%D0%B0%D1%87%D1%87%D0%B8%D0%B9%D0%BD_%D1%82%D0%BE%D0%BE" title="Фибоначчийн тоо – mongolščina" lang="mn" hreflang="mn" data-title="Фибоначчийн тоо" data-language-autonym="Монгол" data-language-local-name="mongolščina" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%AB%E0%A4%BF%E0%A4%AC%E0%A5%8B%E0%A4%A8%E0%A4%BE%E0%A4%9A%E0%A5%80_%E0%A4%B6%E0%A5%8D%E0%A4%B0%E0%A5%87%E0%A4%A3%E0%A5%80" title="फिबोनाची श्रेणी – maratščina" lang="mr" hreflang="mr" data-title="फिबोनाची श्रेणी" data-language-autonym="मराठी" data-language-local-name="maratščina" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-nl badge-Q70894304 mw-list-item" title=""><a href="https://nl.wikipedia.org/wiki/Fibonaccigetal" title="Fibonaccigetal – nizozemščina" lang="nl" hreflang="nl" data-title="Fibonaccigetal" data-language-autonym="Nederlands" data-language-local-name="nizozemščina" 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/Fibonaccitall" title="Fibonaccitall – knjižna norveščina" lang="nb" hreflang="nb" data-title="Fibonaccitall" data-language-autonym="Norsk bokmål" data-language-local-name="knjižna norveščina" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%AB%E0%A8%BC%E0%A9%80%E0%A8%AC%E0%A9%8B%E0%A8%A8%E0%A8%BE%E0%A8%9A%E0%A9%80_%E0%A8%A4%E0%A8%B0%E0%A8%A4%E0%A9%80%E0%A8%AC" title="ਫ਼ੀਬੋਨਾਚੀ ਤਰਤੀਬ – pandžabščina" lang="pa" hreflang="pa" data-title="ਫ਼ੀਬੋਨਾਚੀ ਤਰਤੀਬ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="pandžabščina" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D9%81%DB%8C%D8%A8%D9%88%D9%86%D8%A7%DA%86%DB%90_%D8%A7%D8%B9%D8%AF%D8%A7%D8%AF" title="فیبوناچې اعداد – paštunščina" lang="ps" hreflang="ps" data-title="فیبوناچې اعداد" data-language-autonym="پښتو" data-language-local-name="paštunščina" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Num%C4%83r_Fibonacci" title="Număr Fibonacci – romunščina" lang="ro" hreflang="ro" data-title="Număr Fibonacci" data-language-autonym="Română" data-language-local-name="romunščina" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A7%D0%B8%D1%81%D0%BB%D0%B0_%D0%A4%D0%B8%D0%B1%D0%BE%D0%BD%D0%B0%D1%87%D1%87%D0%B8" title="Числа Фибоначчи – ruščina" lang="ru" hreflang="ru" data-title="Числа Фибоначчи" data-language-autonym="Русский" data-language-local-name="ruščina" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Fibonaccijev_niz" title="Fibonaccijev niz – srbohrvaščina" lang="sh" hreflang="sh" data-title="Fibonaccijev niz" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="srbohrvaščina" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B7%86%E0%B7%92%E0%B6%B6%E0%B7%9C%E0%B6%B1%E0%B7%8F%E0%B6%A0%E0%B7%8A%E0%B6%A0%E0%B7%92_%E0%B7%83%E0%B6%82%E0%B6%9B%E0%B7%8A%E2%80%8D%E0%B6%BA%E0%B7%8F" title="ෆිබොනාච්චි සංඛ්‍යා – sinhalščina" lang="si" hreflang="si" data-title="ෆිබොනාච්චි සංඛ්‍යා" data-language-autonym="සිංහල" data-language-local-name="sinhalščina" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Fibonacci_number" title="Fibonacci number – Simple English" lang="en-simple" hreflang="en-simple" data-title="Fibonacci number" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Numrat_e_Fibonaccit" title="Numrat e Fibonaccit – albanščina" lang="sq" hreflang="sq" data-title="Numrat e Fibonaccit" data-language-autonym="Shqip" data-language-local-name="albanščina" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A4%D0%B8%D0%B1%D0%BE%D0%BD%D0%B0%D1%87%D0%B8%D1%98%D0%B5%D0%B2_%D0%BD%D0%B8%D0%B7" title="Фибоначијев низ – srbščina" lang="sr" hreflang="sr" data-title="Фибоначијев низ" data-language-autonym="Српски / srpski" data-language-local-name="srbščina" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Fibonaccital" title="Fibonaccital – švedščina" lang="sv" hreflang="sv" data-title="Fibonaccital" data-language-autonym="Svenska" data-language-local-name="švedščina" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AA%E0%AE%BF%E0%AE%AA%E0%AE%A9%E0%AE%BE%E0%AE%9A%E0%AF%8D%E0%AE%9A%E0%AE%BF_%E0%AE%8E%E0%AE%A3%E0%AF%8D%E0%AE%95%E0%AE%B3%E0%AF%8D" title="பிபனாச்சி எண்கள் – tamilščina" lang="ta" hreflang="ta" data-title="பிபனாச்சி எண்கள்" data-language-autonym="தமிழ்" data-language-local-name="tamilščina" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%AB%E0%B0%BF%E0%B0%AC%E0%B1%8B%E0%B0%A8%E0%B0%BE%E0%B0%9A%E0%B1%80_%E0%B0%B8%E0%B0%82%E0%B0%96%E0%B1%8D%E0%B0%AF%E0%B0%B2%E0%B1%81" title="ఫిబోనాచీ సంఖ్యలు – telugijščina" lang="te" hreflang="te" data-title="ఫిబోనాచీ సంఖ్యలు" data-language-autonym="తెలుగు" data-language-local-name="telugijščina" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B8%9F%E0%B8%B5%E0%B9%82%E0%B8%9A%E0%B8%99%E0%B8%B1%E0%B8%8A%E0%B8%8A%E0%B8%B5" title="จำนวนฟีโบนัชชี – tajščina" lang="th" hreflang="th" data-title="จำนวนฟีโบนัชชี" data-language-autonym="ไทย" data-language-local-name="tajščina" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Bilang_na_Fibonacci" title="Bilang na Fibonacci – tagalogščina" lang="tl" hreflang="tl" data-title="Bilang na Fibonacci" data-language-autonym="Tagalog" data-language-local-name="tagalogščina" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-uk badge-Q70894304 mw-list-item" title=""><a href="https://uk.wikipedia.org/wiki/%D0%A7%D0%B8%D1%81%D0%BB%D0%B0_%D0%A4%D1%96%D0%B1%D0%BE%D0%BD%D0%B0%D1%87%D1%87%D1%96" title="Числа Фібоначчі – ukrajinščina" lang="uk" hreflang="uk" data-title="Числа Фібоначчі" data-language-autonym="Українська" data-language-local-name="ukrajinščina" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Fibonacci_sonlari" title="Fibonacci sonlari – uzbeščina" lang="uz" hreflang="uz" data-title="Fibonacci sonlari" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbeščina" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/D%C3%A3y_Fibonacci" title="Dãy Fibonacci – vietnamščina" lang="vi" hreflang="vi" data-title="Dãy Fibonacci" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamščina" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Ihap_Fibonacci" title="Ihap Fibonacci – varajščina" lang="war" hreflang="war" data-title="Ihap Fibonacci" data-language-autonym="Winaray" data-language-local-name="varajščina" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%96%90%E6%B3%A2%E9%82%A3%E5%A5%91%E6%95%B0" title="斐波那契数 – kitajščina" lang="zh" hreflang="zh" data-title="斐波那契数" data-language-autonym="中文" data-language-local-name="kitajščina" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E8%B2%BB%E6%B0%8F%E6%95%B8" title="費氏數 – kantonščina" lang="yue" hreflang="yue" data-title="費氏數" data-language-autonym="粵語" data-language-local-name="kantonščina" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q47577#sitelinks-wikipedia" title="Uredi medjezikovne povezave" class="wbc-editpage">Uredi povezave</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Imenski prostori"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet 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data-event-name="pinnable-header.vector-appearance.unpin">skrij</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">Iz Wikipedije, proste enciklopedije</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="sl" dir="ltr"><p><b>Fibonaccijeva <a href="/wiki/%C5%A0tevilo" title="Število">števila</a></b>, ki določajo <b>Fibonaccijevo zaporedje</b>, so v <a href="/wiki/Matematika" title="Matematika">matematiki</a> <a href="/wiki/Rekurzija" title="Rekurzija">rekurzivno</a> določena z naslednjimi <a href="/wiki/Ena%C4%8Dba" title="Enačba">enačbami</a>: </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 F_{n}\equiv F(n)=\left\{{\begin{matrix}1;\,\qquad \qquad \qquad \quad \,\ \ \,&&n=0\,;\ \ \\1;\qquad \qquad \qquad \qquad \,&&n=1;\ \ \,\\F(n-2)+F(n-1);&&n>1.\end{matrix}}\right.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>≡</mo> <mi>F</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow> <mo>{</mo> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>1</mn> <mo>;</mo> <mspace width="thinmathspace" /> <mspace width="2em" /> <mspace width="2em" /> <mspace width="2em" /> <mspace width="1em" /> <mspace width="thinmathspace" /> <mtext> </mtext> <mtext> </mtext> <mspace width="thinmathspace" /> </mtd> <mtd /> <mtd> <mi>n</mi> <mo>=</mo> <mn>0</mn> <mspace width="thinmathspace" /> <mo>;</mo> <mtext> </mtext> <mtext> </mtext> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> <mo>;</mo> <mspace width="2em" /> <mspace width="2em" /> <mspace width="2em" /> <mspace width="2em" /> <mspace width="thinmathspace" /> </mtd> <mtd /> <mtd> <mi>n</mi> <mo>=</mo> <mn>1</mn> <mo>;</mo> <mtext> </mtext> <mtext> </mtext> <mspace width="thinmathspace" /> </mtd> </mtr> <mtr> <mtd> <mi>F</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo>−</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mo>+</mo> <mi>F</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>;</mo> </mtd> <mtd /> <mtd> <mi>n</mi> <mo>></mo> <mn>1.</mn> </mtd> </mtr> </mtable> </mrow> <mo fence="true" stretchy="true" symmetric="true"></mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{n}\equiv F(n)=\left\{{\begin{matrix}1;\,\qquad \qquad \qquad \quad \,\ \ \,&&n=0\,;\ \ \\1;\qquad \qquad \qquad \qquad \,&&n=1;\ \ \,\\F(n-2)+F(n-1);&&n>1.\end{matrix}}\right.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0e42f1e58362c5a326df63b0e21e1dd26fc1dae7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.171ex; width:50.938ex; height:9.509ex;" alt="{\displaystyle F_{n}\equiv F(n)=\left\{{\begin{matrix}1;\,\qquad \qquad \qquad \quad \,\ \ \,&&n=0\,;\ \ \\1;\qquad \qquad \qquad \qquad \,&&n=1;\ \ \,\\F(n-2)+F(n-1);&&n>1.\end{matrix}}\right.}"></span></dd></dl> <p>Zaporedje začnemo z dvema številoma, običajno 1 in 1. Naslednje Fibonaccijevo število dobimo, če seštejemo predhodni. Prva Fibonaccijeva števila so (<a href="/w/index.php?title=Spletna_enciklopedija_celo%C5%A1tevilskih_zaporedij&action=edit&redlink=1" class="new" title="Spletna enciklopedija celoštevilskih zaporedij (stran ne obstaja)">OEIS</a> <span class="nowrap external"><a href="//oeis.org/A000045" class="extiw" title="oeis:A000045">A000045</a></span>):<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><table class="wikitable" style="text-align:right"> <tbody><tr> <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 F_{0}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{0}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/66b39dd19b92e54590febfeab57ed3f1ff40a82b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.936ex; height:2.509ex;" alt="{\displaystyle F_{0}\,}"></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 F_{1}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{1}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ce28b49d78119669a771b8263d98eadd9448cc4d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.936ex; height:2.509ex;" alt="{\displaystyle F_{1}\,}"></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 F_{2}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{2}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c390ee594a338120d6c07259865e1fa3b8d84a3c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.936ex; height:2.509ex;" alt="{\displaystyle F_{2}\,}"></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 F_{3}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{3}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b003a3e56d7ed3dbbec89cd0d6afec896e2b4167" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.936ex; height:2.509ex;" alt="{\displaystyle F_{3}\,}"></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 F_{4}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{4}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4864769a6741de4daeb2a7242c062c5f371c5d28" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.936ex; height:2.509ex;" alt="{\displaystyle F_{4}\,}"></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 F_{5}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{5}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/edf9637879b1a11352b9e2a7faa4fdb3fcd95cd5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.936ex; height:2.509ex;" alt="{\displaystyle F_{5}\,}"></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 F_{6}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{6}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d23a7cff77028f3b630ff8157f0819f136e3a394" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.936ex; height:2.509ex;" alt="{\displaystyle F_{6}\,}"></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 F_{7}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{7}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/684352a408a92022467314884f1d7d14d368781e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.936ex; height:2.509ex;" alt="{\displaystyle F_{7}\,}"></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 F_{8}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{8}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d1dfd1861753498878647f00935ca1d641245e7b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.936ex; height:2.509ex;" alt="{\displaystyle F_{8}\,}"></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 F_{9}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>9</mn> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{9}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e6a998d398a0cd919d398bd03faeee9cd76fad4f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.936ex; height:2.509ex;" alt="{\displaystyle F_{9}\,}"></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 F_{10}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{10}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e9d5bbc46d7190b1c5481c6e11b2664d315efbdc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.758ex; height:2.509ex;" alt="{\displaystyle F_{10}\,}"></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 F_{11}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>11</mn> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{11}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/514b597c544daf70b57ca540ef932ce2d3a0edfc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.758ex; height:2.509ex;" alt="{\displaystyle F_{11}\,}"></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 F_{12}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>12</mn> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{12}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ba39208faab91f197d86dceaca2014cce63c5f3a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.758ex; height:2.509ex;" alt="{\displaystyle F_{12}\,}"></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 F_{13}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>13</mn> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{13}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cee53332e9356bf462bc1ffc48249d1102c26456" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.758ex; height:2.509ex;" alt="{\displaystyle F_{13}\,}"></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 F_{14}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>14</mn> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{14}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/feaa0663acf6b30900f9ce3bbe759ff55bbe5e46" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.758ex; height:2.509ex;" alt="{\displaystyle F_{14}\,}"></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 F_{15}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>15</mn> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{15}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8003c1341947ac7df6343270bd1c4edf3bb9e814" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.758ex; height:2.509ex;" alt="{\displaystyle F_{15}\,}"></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 F_{16}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>16</mn> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{16}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bfd98e763b2871c02ce80835592002369ad8e589" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.758ex; height:2.509ex;" alt="{\displaystyle F_{16}\,}"></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 F_{17}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>17</mn> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{17}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86021238a35737a2a92689b05235210a7cd9e7e2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.758ex; height:2.509ex;" alt="{\displaystyle F_{17}\,}"></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 F_{18}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>18</mn> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{18}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/54fd373c7d2f47004c22bc38cb15e0e3c2901d96" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.758ex; height:2.509ex;" alt="{\displaystyle F_{18}\,}"></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 F_{19}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>19</mn> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{19}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/497899e923672a7500d8b8c4196ea13af429f1a9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.758ex; height:2.509ex;" alt="{\displaystyle F_{19}\,}"></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 F_{20}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>20</mn> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{20}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/906f5127735bf73305200cd1debd10e12fda0d75" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.758ex; height:2.509ex;" alt="{\displaystyle F_{20}\,}"></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 F_{21}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>21</mn> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{21}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d1801a61a46ed6fb35f5d230793b96bb1975b6f2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.758ex; height:2.509ex;" alt="{\displaystyle F_{21}\,}"></span> </td></tr> <tr> <td>1</td> <td><b>1</b></td> <td>2</td> <td>3</td> <td>5 </td> <td>8</td> <td>13</td> <td>21</td> <td>34 </td> <td>55</td> <td>89</td> <td>144</td> <td>233 </td> <td>377</td> <td>610</td> <td>987</td> <td>1597 </td> <td>2584</td> <td>4181</td> <td>6765</td> <td>10946</td> <td>17711 </td></tr></tbody></table></dd></dl> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Slika:FibonacciBlocks.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/95/FibonacciBlocks.svg/200px-FibonacciBlocks.svg.png" decoding="async" width="200" height="126" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/95/FibonacciBlocks.svg/300px-FibonacciBlocks.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/95/FibonacciBlocks.svg/400px-FibonacciBlocks.svg.png 2x" data-file-width="270" data-file-height="170" /></a><figcaption><a href="/wiki/Teselacija" title="Teselacija">Pokritje</a> ravnine s kvadrati v velikosti Fibonaccijevih števil</figcaption></figure> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Slika:Yupana_1.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/98/Yupana_1.png/200px-Yupana_1.png" decoding="async" width="200" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/98/Yupana_1.png/300px-Yupana_1.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/98/Yupana_1.png/400px-Yupana_1.png 2x" data-file-width="1280" data-file-height="960" /></a><figcaption>Jupana (<a href="/wiki/Ke%C4%8Duan%C5%A1%C4%8Dina" title="Kečuanščina">kečuansko</a> za <i>orodje za štetje</i>) je računalo, ki so ga uporabljali <a href="/wiki/Inki" title="Inki">Inki</a>. Raziskovalci menijo da so računi temeljili na Fibonaccijevih številih da se je zmanjšalo število potrebnih zrn na polje.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup></figcaption></figure> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Slika:Fibonacci_spiral_34.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/93/Fibonacci_spiral_34.svg/200px-Fibonacci_spiral_34.svg.png" decoding="async" width="200" height="127" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/93/Fibonacci_spiral_34.svg/300px-Fibonacci_spiral_34.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/93/Fibonacci_spiral_34.svg/400px-Fibonacci_spiral_34.svg.png 2x" data-file-width="915" data-file-height="579" /></a><figcaption>Fibonaccijeva spirala tvorjena z risanjem lokov, ki povezujejo nasprotni oglišči kvadratov v Fibonaccijevem pokritju. Tu so kvadrati velikosti 1, 1, 2, 3, 5, 8, 13, 21 in 34; glej <a href="/wiki/Zlata_spirala" title="Zlata spirala">zlata spirala</a></figcaption></figure> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Slika:Liber_abbaci_magliab_f124r.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/04/Liber_abbaci_magliab_f124r.jpg/200px-Liber_abbaci_magliab_f124r.jpg" decoding="async" width="200" height="306" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/04/Liber_abbaci_magliab_f124r.jpg/300px-Liber_abbaci_magliab_f124r.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/04/Liber_abbaci_magliab_f124r.jpg/400px-Liber_abbaci_magliab_f124r.jpg 2x" data-file-width="744" data-file-height="1137" /></a><figcaption>Stran iz <a href="/wiki/Leonardo_Fibonacci" title="Leonardo Fibonacci">Fibonaccijevega</a> dela <i>Knjiga o abaku</i> (<i><a href="/w/index.php?title=Liber_Abaci&action=edit&redlink=1" class="new" title="Liber Abaci (stran ne obstaja)">Liber Abaci</a></i>; <a href="/w/index.php?title=Narodna_osrednja_knji%C5%BEnica_(Firence)&action=edit&redlink=1" class="new" title="Narodna osrednja knjižnica (Firence) (stran ne obstaja)">Narodna osrednja knjižnica v Firencah</a>) prikazuje Fibonaccijevo zaporedje (uokvirjeno desno) s členi od 0 do 12 označenimi s črno z <a href="/wiki/Rimske_%C5%A1tevilke" title="Rimske številke">rimskimi</a> in z vrednostmi označenimi z rdečo z <a href="/wiki/Arabske_%C5%A1tevilke" title="Arabske številke">indoarabskimi številkami</a></figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><span><audio id="mwe_player_0" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" style="width:220px;" data-durationhint="17" data-mwtitle="Fibonacci.ogg" data-mwprovider="wikimediacommons" resource="/wiki/Slika:Fibonacci.ogg"><source src="//upload.wikimedia.org/wikipedia/commons/9/97/Fibonacci.ogg" type="audio/ogg; codecs="vorbis"" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/97/Fibonacci.ogg/Fibonacci.ogg.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /></audio></span><figcaption>Fibonaccijevo zaporedje zvokovno, <a href="/wiki/Interval_(glasba)" title="Interval (glasba)">harmonični intervali</a> naraščajo, melodični pa padajo.</figcaption></figure> <p>To <a href="/wiki/Zaporedje" title="Zaporedje">zaporedje</a> je prvi opisal <a href="/wiki/Leonardo_Fibonacci" title="Leonardo Fibonacci">Leonardo Fibonacci</a> pri opisu rasti določenega števila zajcev. Števila opisujejo število parov idealiziranega števila zajcev po <i>n</i> mesecih, če upoštevamo: </p> <ul><li>prvi mesec se rodi samo en nov par,</li> <li>novorojeni pari so plodni od svojega drugega meseca naprej,</li> <li>vsak mesec vsak ploden par zaplodi nov par in</li> <li>zajci nikoli ne umrejo.</li></ul> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading3"><h3 id="Enačba"><span id="Ena.C4.8Dba"></span>Enačba</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Fibonaccijevo_%C5%A1tevilo&veaction=edit&section=1" title="Uredi razdelek: Enačba" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Fibonaccijevo_%C5%A1tevilo&action=edit&section=1" title="Urejanje izvorne kode razdelka: Enačba"><span>uredi kodo</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Izraz <b><a href="/wiki/Fibonaccijevo_zaporedje" class="mw-redirect" title="Fibonaccijevo zaporedje">Fibonaccijevega zaporedja</a></b> lahko uporabimo splošneje na vsaki <a href="/wiki/Funkcija" class="mw-redirect" title="Funkcija">funkciji</a> <i>g</i>, kjer je <i>g</i>(<i>n</i> + 2) = <i>g</i>(<i>n</i>) + <i>g</i>(<i>n</i> + 1). Te funkcije so natanko tiste oblike <i>g</i>(<i>n</i>) = <i>aF</i>(<i>n</i>) + <i>bF</i>(<i>n</i> + 1) za poljubna števila <i>a</i> in <i>b</i>, tako da Fibonaccijeva zaporedja tvorijo <a href="/wiki/Vektorski_prostor" title="Vektorski prostor">vektorski prostor</a> s funkcijami <i>F</i>(<i>n</i>) in <i>F</i>(<i>n</i> + 1) kot baza. </p><p>Kot je pokazal <a href="/wiki/Johannes_Kepler" title="Johannes Kepler">Kepler</a>, stopnja rasti Fibonaccijevih števil, <i>F</i>(<i>n</i> + 1) / <i>F</i>(<i>n</i>), <a href="/wiki/Konvergenca" class="mw-redirect mw-disambig" title="Konvergenca">konvergira</a> k <a href="/wiki/%C5%A0tevilo_zlatega_reza" title="Število zlatega reza">številu zlatega reza</a>, označenem z φ. To je pozitivni koren kvadratne enačbe <i>x</i><sup>2</sup> - <i>x</i> - 1 = 0, tako da je φ<sup>2</sup> = φ + 1. Če pomnožimo obe strani z φ<sup><i>n</i></sup>, dobimo φ<sup><i>n</i>+2</sup> = φ<sup><i>n</i>+1</sup> + φ<sup><i>n</i></sup>, in je funkcija φ<sup><i>n</i></sup> Fibonaccijevo zaporedje. Lahko se pokaže, da ima negativni koren kvadratne enačbe, 1 - φ, enake značilnosti. Zato funkciji φ<sup><i>n</i></sup> in (1-φ)<sup><i>n</i></sup> tvorita novo bazo istega prostora. </p><p>Z nastavitvijo koeficientov za primerne začetne vrednosti <i>F</i>(0) = 1 in <i>F</i>(1) = 1, dobimo: </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 F\left(n\right)={\phi ^{n} \over {\sqrt {5}}}-{(1-\phi )^{n} \over {\sqrt {5}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>ϕ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>5</mn> </msqrt> </mrow> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <mi>ϕ</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>5</mn> </msqrt> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F\left(n\right)={\phi ^{n} \over {\sqrt {5}}}-{(1-\phi )^{n} \over {\sqrt {5}}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e0a24f26e135cb74454acec907a759fa3acedd51" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:25.104ex; height:6.676ex;" alt="{\displaystyle F\left(n\right)={\phi ^{n} \over {\sqrt {5}}}-{(1-\phi )^{n} \over {\sqrt {5}}}.}"></span></dd></dl> <p>Isti rezultat dobimo, če uporabimo postopke <a href="/w/index.php?title=Rodovna_funkcija&action=edit&redlink=1" class="new" title="Rodovna funkcija (stran ne obstaja)">rodovnih funkcij</a> ali reševanja linearnih <a href="/wiki/Rekuren%C4%8Dna_ena%C4%8Dba" class="mw-redirect" title="Rekurenčna enačba">rekurenčnih enačb</a>. </p><p>Ko gre <i>n</i> v neskončnost, drugi člen konvergira proti nič, tako, da Fibonaccijeva števila težijo k eksponentu φ<sup><i>n</i></sup> / √5, in zaradi tega njihova razmerja konvergirajo. V bistvu je drugi člen dovolj majhen in lahko dobimo Fibonaccijeva števila samo iz prvega člena, če jih zaokrožamo na najbližje <a href="/wiki/Celo_%C5%A1tevilo" title="Celo število">celo število</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Računanje_Fibonaccijevih_števil"><span id="Ra.C4.8Dunanje_Fibonaccijevih_.C5.A1tevil"></span>Računanje Fibonaccijevih števil</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Fibonaccijevo_%C5%A1tevilo&veaction=edit&section=2" title="Uredi razdelek: Računanje Fibonaccijevih števil" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Fibonaccijevo_%C5%A1tevilo&action=edit&section=2" title="Urejanje izvorne kode razdelka: Računanje Fibonaccijevih števil"><span>uredi kodo</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Računanje Fibonaccijevih števil z računanjem potenc števila zlatega reza ni preveč praktično, razen za majhne vrednosti <i>n</i>, ker se bodo zaokrožitvene napake povečale in števila s tekočo vejico po navadi niso dovolj točna. </p><p>Tudi neposredna rekurzivna uporaba določitve Fibonaccijevega zaporedja ni preveč prikladna, ker moramo računati preveč vrednosti zaporedoma (razen če programski jezik dovoljuje shrambo predhodnih vrednosti fukcije). Zato po navadi računamo Fibonaccijeva števila od spodaj navzgor. Začnemo z vrednostima 1 in 1, potem pa izmenoma zamenjujemo prvo število z drugim, drugo število pa z vsoto prejšnjih dveh. </p><p>Za velike vrednosti in, če uporabimo programski jezik z možnostjo računanja velikih števil, je hitrejša pot računanja Fibonaccijevih števil z naslednjo matrično enačbo: </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 {\begin{bmatrix}1&1\\1&0\end{bmatrix}}^{n}={\begin{bmatrix}F\left(n+1\right)&F\left(n\right)\\F\left(n\right)&F\left(n-1\right)\end{bmatrix}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>F</mi> <mrow> <mo>(</mo> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mtd> <mtd> <mi>F</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>F</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </mtd> <mtd> <mi>F</mi> <mrow> <mo>(</mo> <mrow> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> <mo>]</mo> </mrow> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{bmatrix}1&1\\1&0\end{bmatrix}}^{n}={\begin{bmatrix}F\left(n+1\right)&F\left(n\right)\\F\left(n\right)&F\left(n-1\right)\end{bmatrix}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/97d0636da1d7702d9c645a2ad26a618d36b30316" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:37.016ex; height:6.176ex;" alt="{\displaystyle {\begin{bmatrix}1&1\\1&0\end{bmatrix}}^{n}={\begin{bmatrix}F\left(n+1\right)&F\left(n\right)\\F\left(n\right)&F\left(n-1\right)\end{bmatrix}},}"></span></dd></dl> <p>ki namesto potenciranja uporablja kvadriranje. </p> <div class="mw-heading mw-heading3"><h3 id="Uporabe">Uporabe</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Fibonaccijevo_%C5%A1tevilo&veaction=edit&section=3" title="Uredi razdelek: Uporabe" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Fibonaccijevo_%C5%A1tevilo&action=edit&section=3" title="Urejanje izvorne kode razdelka: Uporabe"><span>uredi kodo</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Fibonaccijeva števila so pomembna pri analizi poteka <a href="/wiki/Evklidov_algoritem" title="Evklidov algoritem">Evklidovega algoritma</a> za določitev <a href="/wiki/Najve%C4%8Dji_skupni_delitelj" title="Največji skupni delitelj">največjega skupnega delitelja</a> dveh celih števil. Izkaže se, da se algoritem najslabše izkaže ravno v primeru, ko določamo največji skupni delitelj dveh zaporednih Fibonaccijevih števil. </p><p><a href="/wiki/Jurij_Vladimirovi%C4%8D_Matijasevi%C4%8D" title="Jurij Vladimirovič Matijasevič">Matijasevič</a> je pokazal, da lahko Fibonaccijeva števila določimo s posebno <a href="/wiki/Diofantska_ena%C4%8Dba" title="Diofantska enačba">diofantsko enačbo</a>, kar nas vodi do njegove izvirne rešitve <a href="/w/index.php?title=Matijasevi%C4%8Dev_izrek&action=edit&redlink=1" class="new" title="Matijasevičev izrek (stran ne obstaja)">10. Hilbertovega problema</a>. </p><p>Fibonaccijeva števila se pojavijo v enačbi za diagonale <a href="/wiki/Pascalov_trikotnik" class="mw-redirect" title="Pascalov trikotnik">Pascalovega trikotnika</a>. </p><p>Zanimiva uporaba Fibonaccijevega zaporedja je pri pretvarjanju <a href="/wiki/Milja" title="Milja">milj</a> v <a href="/wiki/Kilometer" title="Kilometer">kilometre</a>. Na primer, če bi radi vedeli koliko kilometrov je 5 milj, vzamemo Fibonaccijevo število (5) in poiščemo naslednje (8). 5 milj je približno 8 kilometrov. To deluje ker je pretvorbeni količnik med miljami in kilometri približno enak φ. </p><p>Logaritmično spiralo lahko poenostavimo, če začnemo v središču kartezičnega koordinatnega sestava, se premaknemo za F(1) enot v desno, za F(2) enot navzgor, za F(3) enot v levo, za F(4) enot navzdol, za F(5) enot v desno in tako naprej. To je podobno konstrukciji, omenjeni v članku o <a href="/wiki/Zlati_rez" title="Zlati rez">zlatem rezu</a>. Fibonaccijeva števila se v naravi pojavijo velikokrat, kadar so logaritmične spirale sestavljene iz nezveznih enot, kot so tiste pri sončnicah ali pri borovih storžih. </p> <div class="mw-heading mw-heading3"><h3 id="Posplošitve"><span id="Posplo.C5.A1itve"></span>Posplošitve</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Fibonaccijevo_%C5%A1tevilo&veaction=edit&section=4" title="Uredi razdelek: Posplošitve" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Fibonaccijevo_%C5%A1tevilo&action=edit&section=4" title="Urejanje izvorne kode razdelka: Posplošitve"><span>uredi kodo</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Posplošitev Fibonaccijevega zaporedja so <a href="/w/index.php?title=Lucasovo_zaporedje&action=edit&redlink=1" class="new" title="Lucasovo zaporedje (stran ne obstaja)">Lucasova zaporedja</a>. Eno vrsto lahko določimo z: </p> <dl><dd><i>L</i>(0) = 0</dd> <dd><i>L</i>(1) = 1</dd> <dd><i>L</i>(<i>n</i>+2) = <i>PL</i>(<i>n</i>+1) + <i>QL</i>(<i>n</i>)</dd></dl> <p>kjer je običajno Fibonaccijevo zaporedje poseben primer <i>P</i> = <i>Q</i> = 1. Druga vrsta Lucasovega zaporedja se začne z <i>L</i>(0) = 2, <i>L</i>(1) = <i>P</i>. Takšna zaporedja se uporabljajo v <a href="/wiki/Teorija_%C5%A1tevil" title="Teorija števil">teoriji števil</a> in dokazovanju <a href="/wiki/Pra%C5%A1tevilo" title="Praštevilo">praštevilskosti</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Algoritem">Algoritem</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Fibonaccijevo_%C5%A1tevilo&veaction=edit&section=5" title="Uredi razdelek: Algoritem" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Fibonaccijevo_%C5%A1tevilo&action=edit&section=5" title="Urejanje izvorne kode razdelka: Algoritem"><span>uredi kodo</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>V <a href="/wiki/Programski_jezik_pascal" class="mw-redirect" title="Programski jezik pascal">pascalu</a> lahko rekurzivni postopek prepišemo neposredno: </p> <div class="mw-highlight mw-highlight-lang-pascal mw-content-ltr" dir="ltr"><pre><span></span><span class="k">function</span><span class="w"> </span><span class="nf">F</span><span class="p">(</span><span class="n">n</span><span class="o">:</span><span class="kt">integer</span><span class="p">)</span><span class="o">:</span><span class="kt">integer</span><span class="o">;</span> <span class="k">begin</span> <span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="k">or</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="k">then</span><span class="w"> </span> <span class="w"> </span><span class="n">F</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span> <span class="w"> </span><span class="k">else</span> <span class="w"> </span><span class="n">F</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="n">F</span><span class="p">(</span><span class="n">n</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">F</span><span class="p">(</span><span class="n">n</span><span class="o">-</span><span class="mi">2</span><span class="p">)</span><span class="o">;</span> <span class="k">end</span><span class="o">;</span><span class="cm">{F}</span> </pre></div> <p>Vendar je taka neposredna uporaba <a href="/wiki/Rekurzija" title="Rekurzija">rekurzije</a> <b>zelo</b> neučinkovita in pravzaprav služi kot šolski primer, kako je ne smemo uporabljati. Učinkovitejši je iterativni postopek: </p> <div class="mw-highlight mw-highlight-lang-pascal mw-content-ltr" dir="ltr"><pre><span></span><span class="k">function</span><span class="w"> </span><span class="nf">F</span><span class="p">(</span><span class="n">n</span><span class="o">:</span><span class="kt">integer</span><span class="p">)</span><span class="o">:</span><span class="kt">integer</span><span class="o">;</span> <span class="k">var</span><span class="w"> </span><span class="n">a</span><span class="o">,</span><span class="n">b</span><span class="o">,</span><span class="n">c</span><span class="o">,</span><span class="n">j</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">integer</span><span class="o">;</span> <span class="k">begin</span> <span class="w"> </span><span class="n">a</span><span class="o">:=</span><span class="mi">1</span><span class="o">;</span><span class="w"> </span><span class="n">b</span><span class="o">:=</span><span class="mi">1</span><span class="o">;</span> <span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="o">:=</span><span class="mi">3</span><span class="w"> </span><span class="k">to</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="k">do</span><span class="w"> </span><span class="k">begin</span> <span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="n">a</span><span class="o">+</span><span class="n">b</span><span class="o">;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="n">b</span><span class="o">;</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="n">c</span><span class="o">;</span> <span class="w"> </span><span class="k">end</span><span class="o">;</span> <span class="w"> </span><span class="n">F</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="n">c</span><span class="o">;</span> <span class="k">end</span><span class="o">;</span><span class="cm">{F}</span> </pre></div> <p>V <a href="/wiki/Java_(programski_jezik)" title="Java (programski jezik)">javi</a> (kot metoda) bi algoritem zgledal tako: </p> <div class="mw-highlight mw-highlight-lang-java mw-content-ltr" dir="ltr"><pre><span></span><span class="kd">static</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">fibonacci</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span> <span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">f</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span><span class="n">f1</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span><span class="n">f2</span><span class="o">=</span><span class="mi">1</span><span class="p">;</span> <span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="o">=</span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o"><=</span><span class="n">n</span><span class="p">;</span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span> <span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="o"><</span><span class="mi">3</span><span class="p">)</span><span class="w"> </span><span class="n">f</span><span class="o">=</span><span class="mi">1</span><span class="p">;</span> <span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span> <span class="w"> </span><span class="n">f</span><span class="o">=</span><span class="n">f1</span><span class="o">+</span><span class="n">f</span><span class="p">;</span> <span class="w"> </span><span class="n">f1</span><span class="o">=</span><span class="n">f2</span><span class="p">;</span> <span class="w"> </span><span class="n">f2</span><span class="o">=</span><span class="n">f</span><span class="p">;</span> <span class="w"> </span><span class="p">}</span> <span class="p">}</span> </pre></div><p>V <a href="/wiki/Python_(programski_jezik)" title="Python (programski jezik)">Pythonu</a>, kot funkcija, bi algoritem zgledal tako:</p><div class="mw-highlight mw-highlight-lang-python3 mw-content-ltr" dir="ltr"><pre><span></span><span class="k">def</span> <span class="nf">fibonacci</span><span class="p">(</span><span class="n">n</span><span class="p">):</span> <span class="k">if</span> <span class="n">n</span> <span class="o"><</span> <span class="mi">3</span><span class="p">:</span> <span class="k">return</span> <span class="mi">1</span> <span class="n">f1</span><span class="p">,</span> <span class="n">f2</span> <span class="o">=</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span> <span class="n">f1</span><span class="p">,</span> <span class="n">f2</span> <span class="o">=</span> <span class="n">f2</span><span class="p">,</span> <span class="n">f1</span> <span class="o">+</span> <span class="n">f2</span> <span class="k">return</span> <span class="n">f2</span> </pre></div> <div class="mw-heading mw-heading2"><h2 id="Fibonaccijeva_števila_v_naravi"><span id="Fibonaccijeva_.C5.A1tevila_v_naravi"></span>Fibonaccijeva števila v naravi</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Fibonaccijevo_%C5%A1tevilo&veaction=edit&section=6" title="Uredi razdelek: Fibonaccijeva števila v naravi" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Fibonaccijevo_%C5%A1tevilo&action=edit&section=6" title="Urejanje izvorne kode razdelka: Fibonaccijeva števila v naravi"><span>uredi kodo</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Slika:Helianthus_whorl.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/44/Helianthus_whorl.jpg/200px-Helianthus_whorl.jpg" decoding="async" width="200" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/44/Helianthus_whorl.jpg/300px-Helianthus_whorl.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/44/Helianthus_whorl.jpg/400px-Helianthus_whorl.jpg 2x" data-file-width="640" data-file-height="480" /></a><figcaption><a href="/wiki/Son%C4%8Dnica" title="Sončnica">Sončnica</a> ima cvetove razporejene v dve družini, pri čemer je v eni 34 spiralnih zavojev, v drugi pa 55 zavojev. (glej tudi <a href="/wiki/Fermatova_spirala" title="Fermatova spirala">Fermatova spirala</a>)</figcaption></figure> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Slika:FibonacciChamomile.PNG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5a/FibonacciChamomile.PNG/200px-FibonacciChamomile.PNG" decoding="async" width="200" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/5/5a/FibonacciChamomile.PNG 1.5x" data-file-width="300" data-file-height="300" /></a><figcaption>Glava cvetlice <a href="/w/index.php?title=Barvilna_pasja_kamilica&action=edit&redlink=1" class="new" title="Barvilna pasja kamilica (stran ne obstaja)">barvilna pasja kamilica</a> (<i><a href="/w/index.php?title=Cota_tinctoria&action=edit&redlink=1" class="new" title="Cota tinctoria (stran ne obstaja)">Cota tinctoria</a></i>) kaže postavitev 21-ih (modro) in 13-ih (zelenomodro) spiralnih zavojev</figcaption></figure> <p>Poleg rasti določenega števila zajcev so Fibonaccijeva števila tudi drugod v naravi,<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> npr. pri številu <a href="/wiki/List_(rastlina)#Venčni_listi" class="mw-redirect" title="List (rastlina)">venčnih listov</a> in v spiralnih strukturah, ki jih mnoge rastline uporabljajo za razporeditev <a href="/wiki/Seme" title="Seme">semen</a> (glej tudi <a href="/wiki/Fermatova_spirala" title="Fermatova spirala">Fermatova spirala</a>). Poleg števila parov zajcev je znan primer tudi število <a href="/wiki/%C4%8Cebela" class="mw-redirect" title="Čebela">čebel</a> pri idealiziranemu razmnoževanju, če upoštevamo da: </p> <ul><li>se iz neoplojenega jajčeca izvali samec,</li> <li>se iz jajčeca, ki ga oplodi samec, izvali samica.</li></ul> <p>Samec bo tako vedno imel enega starša, samica pa dva. Če analiziramo število prednikov kateregakoli samca (1), bo ta imel vedno enega starša, tj. samico (1). Slednja ima dva starša, samca in samico (2), ta samec pa bo prav tako imel enega starša in samica dva starša, kar da število 3.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> V praksi se še danes uporablja izpopolnjene različice Fibonaccijeve sheme pri preučevanju drugih <a href="/wiki/%C5%BDivali" title="Živali">živalskih</a> <a href="/wiki/Populacija" class="mw-redirect" title="Populacija">populacij</a>. </p><p>Pri nekaterih <a href="/wiki/Cvetnice" class="mw-redirect" title="Cvetnice">cvetnicah</a> so ta števila jasno izražena pri venčnih listih. Tako imajo <a href="/w/index.php?title=Lilije&action=edit&redlink=1" class="new" title="Lilije (stran ne obstaja)">lilije</a> 3 venčne liste, <a href="/wiki/Zlatica" title="Zlatica">zlatice</a> 5, <a href="/w/index.php?title=Ostro%C5%BEnik_(rastlina)&action=edit&redlink=1" class="new" title="Ostrožnik (rastlina) (stran ne obstaja)">ostrožniki</a> pogosto 8, <a href="/wiki/Ognji%C4%8D" class="mw-redirect" title="Ognjič">ognjič</a> 13, <a href="/w/index.php?title=Aster&action=edit&redlink=1" class="new" title="Aster (stran ne obstaja)">astre</a> 21 in <a href="/wiki/Navadna_marjetica" title="Navadna marjetica">marjetice</a> ter <a href="/wiki/Son%C4%8Dnica" title="Sončnica">sončnice</a> navadno po 34, 55 ali 89 listov. Lahko se pojavijo manj običajna števila, in sicer dvojna Fibonaccijeva števila, kar je posledica tehnike gojenja rastlin, ki podvoji število listov, ali pa podobna nepravilna zaporedja (npr. 1, 3, 4, 7, 18, ...). Pri razporeditvi semen so znani primer sončnice, ki imajo semena razporejena v dve družini, pri čemer je v manjših sončnicah v eni družini 34 spiralnih zavojev, v drugi pa 55, pri večjih pa sta ti dve števili 55 in 89 ali 89 in 144. Tudi luske na <a href="/wiki/Jelka_(rod)" title="Jelka (rod)">jelovih</a> <a href="/wiki/Stor%C5%BE" title="Storž">storžih</a> so tipično razporejene v dveh družinah prepletenih spiral; storž <a href="/w/index.php?title=Norve%C5%A1ka_jelka&action=edit&redlink=1" class="new" title="Norveška jelka (stran ne obstaja)">norveške jelke</a> ima tako 5 zavojev lusk v eni družini, v drugi pa 3.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Fibonaccijeva_števila_v_leposlovju"><span id="Fibonaccijeva_.C5.A1tevila_v_leposlovju"></span>Fibonaccijeva števila v leposlovju</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Fibonaccijevo_%C5%A1tevilo&veaction=edit&section=7" title="Uredi razdelek: Fibonaccijeva števila v leposlovju" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Fibonaccijevo_%C5%A1tevilo&action=edit&section=7" title="Urejanje izvorne kode razdelka: Fibonaccijeva števila v leposlovju"><span>uredi kodo</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Fibonaccijeva števila je uporabil <a href="/wiki/Dan_Brown" title="Dan Brown">Dan Brown</a> v svoji knjigi <i><a href="/wiki/Da_Vincijeva_%C5%A1ifra" class="mw-redirect" title="Da Vincijeva šifra">Da Vincijeva šifra</a></i>. </p> <div class="mw-heading mw-heading2"><h2 id="Glej_tudi">Glej tudi</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Fibonaccijevo_%C5%A1tevilo&veaction=edit&section=8" title="Uredi razdelek: Glej tudi" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Fibonaccijevo_%C5%A1tevilo&action=edit&section=8" title="Urejanje izvorne kode razdelka: Glej tudi"><span>uredi kodo</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Obratna_Fibonaccijeva_konstanta" title="Obratna Fibonaccijeva konstanta">obratna Fibonaccijeva konstanta</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Sklici">Sklici</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Fibonaccijevo_%C5%A1tevilo&veaction=edit&section=9" title="Uredi razdelek: Sklici" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Fibonaccijevo_%C5%A1tevilo&action=edit&section=9" title="Urejanje izvorne kode razdelka: Sklici"><span>uredi kodo</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist columns references-column-width" style="column-width: 30em; list-style-type: decimal;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text"><a class="mw-selflink-fragment" href="#CITEREFKnott1996-2011"> Knott (1996-2011)</a>.</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r5980307">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"»""«""›""‹"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free a,.mw-parser-output .citation .cs1-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited a,.mw-parser-output .id-lock-registration a,.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription a,.mw-parser-output .citation .cs1-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:#d33}.mw-parser-output .cs1-visible-error{color:#d33}.mw-parser-output .cs1-maint{display:none;color:#3a3;margin-left:0.3em}.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}</style><cite id="CITEREFAimiDe_Pasquale" class="citation web cs1 cs1-prop-foreign-lang-source">Aimi, Antonio; De Pasquale, Nicolino. <a rel="nofollow" class="external text" href="http://www.quipus.it/english/Andean%20Calculators.pdf">»ANDEAN CALCULATORS«</a> <span class="cs1-format">(PDF)</span> (v angleščini).</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=neznano&rft.btitle=ANDEAN+CALCULATORS&rft.aulast=Aimi&rft.aufirst=Antonio&rft.au=De+Pasquale%2C+Nicolino&rft_id=http%3A%2F%2Fwww.quipus.it%2Fenglish%2FAndean%2520Calculators.pdf&rfr_id=info%3Asid%2Fsl.wikipedia.org%3AFibonaccijevo+%C5%A1tevilo" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text"><a class="mw-selflink-fragment" href="#CITEREFDouadyCouder1996"> Douady; Couder (1996)</a>.</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><a href="#cite_ref-4">↑</a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5980307"><cite class="citation web cs1 cs1-prop-foreign-lang-source"><a rel="nofollow" class="external text" href="http://american-university.com/cas/mathstat/newstudents/shared/puzzles/fibbee.html">»The Fibonacci Numbers and the Ancestry of Bees«</a> (v angleščini)<span class="reference-accessdate">. Pridobljeno 3. decembra 2009</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=neznano&rft.btitle=The+Fibonacci+Numbers+and+the+Ancestry+of+Bees&rft_id=http%3A%2F%2Famerican-university.com%2Fcas%2Fmathstat%2Fnewstudents%2Fshared%2Fpuzzles%2Ffibbee.html&rfr_id=info%3Asid%2Fsl.wikipedia.org%3AFibonaccijevo+%C5%A1tevilo" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><a href="#cite_ref-5">↑</a></span> <span class="reference-text"><a class="mw-selflink-fragment" href="#CITEREFPrusinkiewiczLindenmayer1990"> Prusinkiewicz; Lindenmayer (1990)</a>.</span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Viri">Viri</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Fibonaccijevo_%C5%A1tevilo&veaction=edit&section=10" title="Uredi razdelek: Viri" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Fibonaccijevo_%C5%A1tevilo&action=edit&section=10" title="Urejanje izvorne kode razdelka: Viri"><span>uredi kodo</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5980307"><cite id="CITEREFDouadyCouder1996" class="citation magazine cs1">Douady, S; Couder, Y. (1996). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20060526054108/http://www.math.ntnu.no/~jarlet/Douady96.pdf">»Phyllotaxis as a Dynamical Self Organizing Process«</a> <span class="cs1-format">(PDF)</span>. <i><a href="/w/index.php?title=Journal_of_Theoretical_Biology&action=edit&redlink=1" class="new" title="Journal of Theoretical Biology (stran ne obstaja)">Journal of Theoretical Biology</a></i>. Zv. 178, št. 178. str. 255–274. <a href="/wiki/Doi_(identifikator)" class="mw-redirect" title="Doi (identifikator)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1006%2Fjtbi.1996.0026">10.1006/jtbi.1996.0026</a>. Arhivirano iz <a rel="nofollow" class="external text" href="http://www.math.ntnu.no/~jarlet/Douady96.pdf">prvotnega spletišča</a> <span class="cs1-format">(PDF)</span> dne 26. maja 2006<span class="reference-accessdate">. Pridobljeno 3. decembra 2009</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=%C4%8Dlanek&rft.jtitle=Journal+of+Theoretical+Biology&rft.atitle=Phyllotaxis+as+a+Dynamical+Self+Organizing+Process&rft.volume=178&rft.issue=178&rft.pages=255-274&rft.date=1996&rft_id=info%3Adoi%2F10.1006%2Fjtbi.1996.0026&rft.aulast=Douady&rft.aufirst=S&rft.au=Couder%2C+Y.&rft_id=http%3A%2F%2Fwww.math.ntnu.no%2F~jarlet%2FDouady96.pdf&rfr_id=info%3Asid%2Fsl.wikipedia.org%3AFibonaccijevo+%C5%A1tevilo" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5980307"><cite id="CITEREFKnott1996–2011" class="citation cs2 cs1-prop-foreign-lang-source">Knott, Ron (1996–2011), »Fib table«, <a rel="nofollow" class="external text" href="http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibtable.html"><i>Fibonacci</i></a> (v angleščini), Združeno kraljestvo: Surrey<span class="reference-accessdate">, pridobljeno 10. maja 2013</span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=knji%C5%BEni+predmet&rft.atitle=Fib+table&rft.btitle=Fibonacci&rft.place=Zdru%C5%BEeno+kraljestvo&rft.pub=Surrey&rft.date=1996%2F2011&rft.aulast=Knott&rft.aufirst=Ron&rft_id=http%3A%2F%2Fwww.maths.surrey.ac.uk%2Fhosted-sites%2FR.Knott%2FFibonacci%2Ffibtable.html&rfr_id=info%3Asid%2Fsl.wikipedia.org%3AFibonaccijevo+%C5%A1tevilo" class="Z3988"></span>. Stran navaja prvih 300 Fibonaccijevih števil 300 F<sub><i>n</i></sub> razstavljenih na prafaktorje in povezavami na druge obsežnejše razpredelnice.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5980307"><cite id="CITEREFPrusinkiewiczLindenmayer1990" class="citation book cs1">Prusinkiewicz, P.; Lindenmayer, A. (1990). <a rel="nofollow" class="external text" href="http://algorithmicbotany.org/papers/#webdocs"><i>The Algorithmic Beauty of Plants</i></a>. Springer-Verlag. str. 101–107. <a href="/wiki/ISBN_(identifikator)" class="mw-redirect" title="ISBN (identifikator)">ISBN</a> <a href="/wiki/Posebno:ViriKnjig/978-0387972978" title="Posebno:ViriKnjig/978-0387972978"><bdi>978-0387972978</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=knjiga&rft.btitle=The+Algorithmic+Beauty+of+Plants&rft.pages=101-107&rft.pub=Springer-Verlag&rft.date=1990&rft.isbn=978-0387972978&rft.aulast=Prusinkiewicz&rft.aufirst=P.&rft.au=Lindenmayer%2C+A.&rft_id=http%3A%2F%2Falgorithmicbotany.org%2Fpapers%2F%23webdocs&rfr_id=info%3Asid%2Fsl.wikipedia.org%3AFibonaccijevo+%C5%A1tevilo" class="Z3988"></span></li></ul> <p><br clear="all" /> </p> <div role="navigation" class="navbox" aria-labelledby="Zaporedja_in_vrste" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" 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vrsta</a></li> <li><a href="/w/index.php?title=Dirichletova_vrsta&action=edit&redlink=1" class="new" title="Dirichletova vrsta (stran ne obstaja)">Dirichletove vrste</a></li> <li><a href="/w/index.php?title=Formalna_poten%C4%8Dna_vrsta&action=edit&redlink=1" class="new" title="Formalna potenčna vrsta (stran ne obstaja)">formalne potenčne vrste</a></li> <li><a href="/wiki/Fourierova_vrsta" title="Fourierova vrsta">Fourierove vrste</a></li> <li><a href="/wiki/Funkcijska_vrsta" title="Funkcijska vrsta">funkcijska vrsta</a></li> <li><a href="/wiki/Lambertova_vrsta" title="Lambertova vrsta">Lambertova vrsta</a></li> <li><a href="/wiki/Laurentova_vrsta" title="Laurentova vrsta">Laurentova vrsta</a></li> <li><a href="/w/index.php?title=Neskon%C4%8Dna_vrsta&action=edit&redlink=1" class="new" title="Neskončna vrsta (stran ne obstaja)">neskončne vrste</a></li> <li><a href="/wiki/Poten%C4%8Dna_vrsta" title="Potenčna vrsta">potenčne vrste</a></li> <li><a href="/wiki/Taylorjeva_vrsta" title="Taylorjeva vrsta">Taylorjeva vrsta</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Hipergeometri%C4%8Dna_funkcija" title="Hipergeometrična funkcija">Hipergeometrične<br /> vrste</a></th><td class="navbox-list navbox-even hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/w/index.php?title=Posplo%C5%A1ena_hipergeometri%C4%8Dna_vrsta&action=edit&redlink=1" class="new" title="Posplošena hipergeometrična vrsta (stran ne obstaja)">posplošene hipergeometrične vrste</a></li> <li><a href="/w/index.php?title=Hipergeometri%C4%8Dna_funkcija_matri%C4%8Dnega_argumenta&action=edit&redlink=1" class="new" title="Hipergeometrična funkcija matričnega argumenta (stran ne obstaja)">hipergeometrična funkcija matričnega argumenta</a></li> <li><a href="/w/index.php?title=Lauricellova_hipergeometri%C4%8Dna_vrsta&action=edit&redlink=1" class="new" title="Lauricellova hipergeometrična vrsta (stran ne obstaja)">Lauricellove hipergeometrične vrste</a></li> <li><a href="/w/index.php?title=Elipti%C4%8Dna_hipergeometri%C4%8Dna_vrsta&action=edit&redlink=1" class="new" title="Eliptična hipergeometrična vrsta (stran ne obstaja)">eliptične hipergeometrične vrste</a></li> <li><a href="/w/index.php?title=Riemannova_diferencialna_ena%C4%8Dba&action=edit&redlink=1" class="new" title="Riemannova diferencialna enačba (stran ne obstaja)">Riemannova diferencialna enačba</a></li> <li><a href="/w/index.php?title=Elipti%C4%8Dna_hipergeometri%C4%8Dna_vrsta&action=edit&redlink=1" class="new" title="Eliptična hipergeometrična vrsta (stran ne obstaja)">hipergeometrične vrste theta</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Celo%C5%A1tevilsko_zaporedje" title="Celoštevilsko zaporedje">Celoštevilska<br /> zaporedja</a></th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/w/index.php?title=Polno_zaporedje&action=edit&redlink=1" class="new" title="Polno zaporedje (stran ne obstaja)">polna zaporedja</a></li> <li><a href="/w/index.php?title=Kub_(algebra)&action=edit&redlink=1" class="new" title="Kub (algebra) (stran ne obstaja)">kubi</a></li> <li><a href="/wiki/Fakulteta_(funkcija)" title="Fakulteta (funkcija)">fakultete</a></li> <li><a href="/wiki/Primoriela" title="Primoriela">primoriele</a></li> <li><a class="mw-selflink selflink">Fibonaccijeva števila</a></li> <li><a href="/w/index.php?title=Fugirativno_%C5%A1tevilo&action=edit&redlink=1" class="new" title="Fugirativno število (stran ne obstaja)">figurativna števila</a></li> <li><a href="/w/index.php?title=Sedemkotni%C5%A1ko_%C5%A1tevilo&action=edit&redlink=1" class="new" title="Sedemkotniško število (stran ne obstaja)">sedemkotniška števila</a></li> <li><a href="/wiki/%C5%A0estkotni%C5%A1ko_%C5%A1tevilo" title="Šestkotniško število">šestkotniška števila</a></li> <li><a href="/w/index.php?title=Seznam_zaporedij_OEIS&action=edit&redlink=1" class="new" title="Seznam zaporedij OEIS (stran ne obstaja)">seznam</a></li> <li><a href="/wiki/Lucasovo_%C5%A1tevilo" class="mw-redirect" title="Lucasovo število">Lucasova števila</a></li> <li><a href="/w/index.php?title=Pellovo_%C5%A1tevilo&action=edit&redlink=1" class="new" title="Pellovo število (stran ne obstaja)">Pellova števila</a></li> <li><a href="/wiki/Petkotni%C5%A1ko_%C5%A1tevilo" title="Petkotniško število">petkotniška števila</a></li> <li><a href="/wiki/Mnogokotni%C5%A1ko_%C5%A1tevilo" title="Mnogokotniško število">mnogokotniška števila</a></li> <li><a href="/wiki/Kvadratno_%C5%A1tevilo" title="Kvadratno število">kvadratna števila</a></li> <li><a href="/wiki/Trikotni%C5%A1ko_%C5%A1tevilo" title="Trikotniško število">trikotniška števila</a></li> <li><a href="/w/index.php?title=Barkerjeva_koda&action=edit&redlink=1" class="new" title="Barkerjeva koda (stran ne obstaja)">Barkerjeva koda</a></li> <li><a href="/w/index.php?title=De_Bruijnovo_zaporedje&action=edit&redlink=1" class="new" title="De Bruijnovo zaporedje (stran ne obstaja)">de Bruijnovo zaporedje</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Druga<br /> zaporedja</th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;padding-left:0em;padding-right:0em;text-align:left"><div style="padding:0em 0.75em;"><a href="/wiki/Divergentna_vrsta" title="Divergentna vrsta">Divergentne vrste</a></div></th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/1_%E2%88%92_2_%2B_3_%E2%88%92_4_%2B_%C2%B7%C2%B7%C2%B7" title="1 − 2 + 3 − 4 + ···">1 − 2 + 3 − 4 + ···</a></li> <li><a href="/w/index.php?title=1_%E2%88%92_1_%2B_2_%E2%88%92_6_%2B_24_%E2%88%92_120_%2B_%C2%B7%C2%B7%C2%B7&action=edit&redlink=1" class="new" title="1 − 1 + 2 − 6 + 24 − 120 + ··· (stran ne obstaja)">1 − 1 + 2 − 6 + 24 − 120 + ···</a></li> <li><a href="/wiki/Harmoni%C4%8Dna_vrsta" title="Harmonična vrsta">1 + 1/2 + 1/3 + 1/4 + ··· (harmonična vrsta)</a></li></ul> </div></td></tr></tbody></table><div> <ul><li><a href="/w/index.php?title=Cauchyjevo_zaporedje&action=edit&redlink=1" class="new" title="Cauchyjevo zaporedje (stran ne obstaja)">Cauchyjevo zaporedje</a></li> <li><a href="/w/index.php?title=Periodi%C4%8Dno_zaporedje&action=edit&redlink=1" class="new" title="Periodično zaporedje (stran ne obstaja)">periodična 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