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The On-Line Encyclopedia of Integer Sequences (OEIS)
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 3.2 Final//EN"> <html> <head> <link rel="stylesheet" href="/styles.css"> <meta name="format-detection" content="telephone=no"> <meta http-equiv="content-type" content="text/html; charset=utf-8"> <meta name=viewport content="width=device-width, initial-scale=1"> <meta name="keywords" content="OEIS,integer sequences,Sloane" /> <title>The On-Line Encyclopedia of Integer Sequences (OEIS)</title> <link rel="search" type="application/opensearchdescription+xml" title="OEIS" href="/oeis.xml"> <script> var myURL = "\/history?seq=A027113" function redir() { var host = document.location.hostname; if(host != "oeis.org" && host != "127.0.0.1" && !/^([0-9.]+)$/.test(host) && host != "localhost" && host != "localhost.localdomain") { document.location = "https"+":"+"//"+"oeis"+".org/" + myURL; } } function sf() { if(document.location.pathname == "/" && document.f) document.f.q.focus(); } </script> </head> <body bgcolor=#ffffff onload="redir();sf()"> <div class=loginbar> <div class=login> <a href="/login?redirect=%2fhistory%3fseq%3dA027113">login</a> </div> </div> <div class=center><div class=top> <center> <div class=donors> The OEIS is supported by <a href="http://oeisf.org/#DONATE">the many generous donors to the OEIS Foundation</a>. </div> <div class=banner> <a href="/"><img class=banner border="0" width="600" src="/banner2021.jpg" alt="The On-Line Encyclopedia of Integer Sequences (OEIS)"></a> </div> </center> </div></div> <div class=center><div class=pagebody> <div class=searchbarcenter> <form name=f action="/search" method="GET"> <div class=searchbargreet> <div class=searchbar> <div class=searchq> <input class=searchbox maxLength=1024 name=q value="" title="Search Query"> </div> <div class=searchsubmit> <input type=submit value="Search" name=go> </div> <div class=hints> <span class=hints><a href="/hints.html">Hints</a></span> </div> </div> <div class=searchgreet> (Greetings from <a href="/welcome">The On-Line Encyclopedia of Integer Sequences</a>!) </div> </div> </form> </div> <center> <h2 style="margin-top:0; margin-bottom:0;"> Revision History for <a href="/A027113">A027113</a> </h2> (Bold, blue-underlined text is an <ins>addition</ins>; faded, red-underlined text is a <del>deletion</del>.) </center> <br> Showing all changes. <br> <div class=history> <div class=space1></div> <div class=line></div> <div class=seqhead> <div class=seqnumname> <div class=seqnum><a href="/A027113">A027113</a></div> <div class=seqname> Triangular array T given by rows: T(n,0)=1 for n >= 0, T(n,1)=1,T(n,2)=2 for n >= 1 and for n >= 2, T(n,k)=T(n-1,k-3)+T(n-1,k-2)+T(n-1,k-1) for 3<=k<=2n-1, T(n,2n)=T(n-1,2n-3)+T(n-1,2n-2). <br> <font size=-1>(<a href="/history?seq=A027113">history</a>; <a href="/A027113">published version</a>) </font> </div> </div> </div> <div class=resultline></div> <div class="revbar"> <a href="/history/view?seq=A027113&v=6">#6</a> by <a href="/history?user=Russ%20Cox">Russ Cox</a> at Fri Mar 30 18:56:14 EDT 2012 </div> <div> <div class=entry> <div class=section> <div class=sectname>AUTHOR</div> <div class=sectbody> <p class="diffs"><tt><del>Clark Kimberling (ck6(AT)evansville.edu)</del></tt></p> <p class="diffs"><tt><ins><a href="/wiki/User:Clark_Kimberling">Clark Kimberling</a></ins></tt></p> </div> </div> </div> </div> <div class="space4"></div> <div class=discussbar> <div class=discusshead>Discussion</div> <div class=discussnote> <div class=date>Fri Mar 30</div> <div class=time>18:56</div> <pre class=note><span class=user>OEIS Server</span>: https://oeis.org/edit/global/285</pre> </div> </div> <div class=space4></div> <div class=resultline></div> <div class="revbar"> <a href="/history/view?seq=A027113&v=5">#5</a> by <a href="/history?user=N.%20J.%20A.%20Sloane">N. J. A. Sloane</a> at Fri Feb 27 03:00:00 EST 2009 </div> <div> <div class=entry> <div class=section> <div class=sectname>NAME</div> <div class=sectbody> <p class="diffs"><tt>Triangular array T given by rows: T(n,0)=1 for n >= 0, T(n,1)=1,T(n,2)=2 for n >= 1<del>,</del><del> </del><ins> </ins>and for n >= 2, T(n,k)=T(n-1,k-3)+T(n-1,k-2)+T(n-1,k-1) for 3<=k<=2n-1, T(n,2n)=T(n-1,2n-3)+T(n-1,2n-2).</tt></p> </div> </div> <div class=section> <div class=sectname>KEYWORD</div> <div class=sectbody> <p class="diffs"><tt><span title="a sequence of nonnegative numbers">nonn</span>,<span title="an irregular (or funny-shaped) array of numbers made into a sequence by reading it row by row">tabf</span><del>,</del><del><span title="added within the last two weeks">new</span></del></tt></p> </div> </div> </div> </div> <div class=space4></div> <div class=resultline></div> <div class="revbar"> <a href="/history/view?seq=A027113&v=4">#4</a> by <a href="/history?user=N.%20J.%20A.%20Sloane">N. J. A. Sloane</a> at Sat Sep 13 03:00:00 EDT 2003 </div> <div> <div class=entry> <div class=section> <div class=sectname>KEYWORD</div> <div class=sectbody> <p class="diffs"><tt><span title="a sequence of nonnegative numbers">nonn</span>,<span title="an irregular (or funny-shaped) array of numbers made into a sequence by reading it row by row">tabf</span><del>,</del><del><span title="added within the last two weeks">new</span></del></tt></p> </div> </div> <div class=section> <div class=sectname>AUTHOR</div> <div class=sectbody> <p class="diffs"><tt>Clark Kimberling<del>,</del><del> </del><ins> </ins><ins>(</ins>ck6(AT)evansville.edu<ins>)</ins></tt></p> </div> </div> </div> </div> <div class=space4></div> <div class=resultline></div> <div class="revbar"> <a href="/history/view?seq=A027113&v=3">#3</a> by <a href="/history?user=N.%20J.%20A.%20Sloane">N. J. A. Sloane</a> at Fri May 16 03:00:00 EDT 2003 </div> <div> <div class=entry> <div class=section> <div class=sectname>NAME</div> <div class=sectbody> <p class="diffs"><tt>Triangular array T given by rows: T(n,0)=1 for n<ins> </ins>>=<ins> </ins>0, T(n,1)=1,T(n,2)=2 for n<ins> </ins>>=<ins> </ins>1, and for n<ins> </ins>>=<ins> </ins>2, T(n,k)=T(n-1,k-3)+T(n-1,k-2)+T(n-1,k-1) for 3<=k<=2n-1, T(n,2n)=T(n-1,2n-3)+T(n-1,2n-2).</tt></p> </div> </div> <div class=section> <div class=sectname>KEYWORD</div> <div class=sectbody> <p class="diffs"><tt><span title="a sequence of nonnegative numbers">nonn</span>,<span title="an irregular (or funny-shaped) array of numbers made into a sequence by reading it row by row">tabf</span><del>,</del><del><span title="added within the last two weeks">new</span></del></tt></p> </div> </div> <div class=section> <div class=sectname>AUTHOR</div> <div class=sectbody> <p class="diffs"><tt>Clark Kimberling, ck6<del>@</del><del>cedar</del><del>.</del><ins>(</ins><ins>AT</ins><ins>)</ins>evansville.edu</tt></p> </div> </div> </div> </div> <div class=space4></div> <div class=resultline></div> <div class="revbar"> <a href="/history/view?seq=A027113&v=2">#2</a> by <a href="/history?user=N.%20J.%20A.%20Sloane">N. J. A. Sloane</a> at Mon May 08 03:00:00 EDT 2000 </div> <div> <div class=entry> <div class=section> <div class=sectname>NAME</div> <div class=sectbody> <p class="diffs"><tt><del>Array</del><del> </del><ins>Triangular</ins><ins> </ins><ins>array</ins><ins> </ins>T given by rows: T(n,0)=1 for n>=0, T(n,1)=1,T(n,2)=2 for n>=1, and for n>=2, T(n,k)=T(n-1,k-3)+T(n-1,k-2)+T(n-1,k-1) for 3<=k<=2n-1, T(n,2n)=T(n-1,2n-3)+T(n-1,2n-2).</tt></p> </div> </div> <div class=section> <div class=sectname>KEYWORD</div> <div class=sectbody> <p class="diffs"><tt><span title="a sequence of nonnegative numbers">nonn</span>,<span title="an irregular (or funny-shaped) array of numbers made into a sequence by reading it row by row">tabf</span><del>,</del><del><span title="added within the last two weeks">new</span></del></tt></p> </div> </div> </div> </div> <div class=space4></div> <div class=resultline></div> <div class="revbar"> <a href="/history/view?seq=A027113&v=1">#1</a> by <a href="/history?user=N.%20J.%20A.%20Sloane">N. J. A. Sloane</a> at Sat Dec 11 03:00:00 EST 1999 </div> <div> <div class=entry> <div class=section> <div class=sectname>NAME</div> <div class=sectbody> <p class="diffs"><tt><ins>Array T given by rows: T(n,0)=1 for n>=0, T(n,1)=1,T(n,2)=2 for n>=1, and for n>=2, T(n,k)=T(n-1,k-3)+T(n-1,k-2)+T(n-1,k-1) for 3<=k<=2n-1, T(n,2n)=T(n-1,2n-3)+T(n-1,2n-2).</ins></tt></p> </div> </div> <div class=section> <div class=sectname>DATA</div> <div class=sectbody> <p class="diffs"><tt><ins>1, 1, 1, 2, 1, 1, 2, 4, 3, 1, 1, 2, 4, 7, 9, 7, 1, 1, 2, 4, 7, 13, 20, 23, 16, 1, 1, 2, 4, 7, 13, 24, 40, 56, 59, 39, 1, 1, 2, 4, 7, 13, 24, 44, 77, 120, 155, 154, 98, 1, 1, 2, 4, 7, 13, 24, 44, 81, 145, 241, 352, 429, 407, 252, 1, 1, 2, 4, 7, 13, 24</ins></tt></p> </div> </div> <div class=section> <div class=sectname>OFFSET</div> <div class=sectbody> <p class="diffs"><tt><ins>1,4</ins></tt></p> </div> </div> <div class=section> <div class=sectname>COMMENTS</div> <div class=sectbody> <p class="diffs"><tt><ins>The rows are of lengths 1, 3, 5, 7, ...</ins></tt></p> </div> </div> <div class=section> <div class=sectname>EXAMPLE</div> <div class=sectbody> <p class="diffs"><tt><ins>1; 1,1,2; 1,1,2,4,3; 1,1,2,4,7,9,7; 1,1,2,4,7,13,20,23,16; ...</ins></tt></p> </div> </div> <div class=section> <div class=sectname>KEYWORD</div> <div class=sectbody> <p class="diffs"><tt><ins><span title="a sequence of nonnegative numbers">nonn</span>,<span title="an irregular (or funny-shaped) array of numbers made into a sequence by reading it row by row">tabf</span></ins></tt></p> </div> </div> <div class=section> <div class=sectname>AUTHOR</div> <div class=sectbody> <p class="diffs"><tt><ins>Clark Kimberling, ck6@cedar.evansville.edu</ins></tt></p> </div> </div> <div class=section> <div class=sectname>STATUS</div> <div class=sectbody> <p class="diffs"><tt><ins>approved</ins></tt></p> </div> </div> </div> </div> <div class=space4></div> <div class=space10></div> </div> </div></div> <p> <div class=footerpad></div> <div class=footer> <center> <div class=bottom> <div class=linksbar> <a href="/">Lookup</a> <a href="/wiki/Welcome"><font color="red">Welcome</font></a> <a href="/wiki/Main_Page"><font color="red">Wiki</font></a> <a href="/wiki/Special:RequestAccount">Register</a> <a href="/play.html">Music</a> <a href="/plot2.html">Plot 2</a> <a href="/demo1.html">Demos</a> <a href="/wiki/Index_to_OEIS">Index</a> <a href="/webcam">WebCam</a> <a href="/Submit.html">Contribute</a> <a href="/eishelp2.html">Format</a> <a href="/wiki/Style_Sheet">Style Sheet</a> <a href="/transforms.html">Transforms</a> <a href="/ol.html">Superseeker</a> <a href="/recent">Recents</a> </div> <div class=linksbar> <a href="/community.html">The OEIS Community</a> </div> <div class=linksbar> Maintained by <a href="http://oeisf.org">The OEIS Foundation Inc.</a> </div> <div class=dbinfo>Last modified November 28 04:00 EST 2024. 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