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A131875 - 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>A131875 - OEIS</title> <link rel="search" type="application/opensearchdescription+xml" title="OEIS" href="/oeis.xml"> <script> var myURL = "\/A131875" 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=%2fA131875">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="A131875 - 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> <div class=sequence> <div class=space1></div> <div class=line></div> <div class=seqhead> <div class=seqnumname> <div class=seqnum> A131875 </div> <div class=seqname> Triangle, <a href="/A000012" title="The simplest sequence of positive numbers: the all 1's sequence.">A000012</a> * <a href="/A131844" title="3*A131821 - 2.">A131844</a> as infinite lower triangular matrices. </div> </div> <div class=scorerefs> 2 </div> </div> <div> <div class=seqdatabox> <div class=seqdata>1, 5, 4, 12, 5, 7, 22, 6, 8, 10, 35, 7, 9, 11, 13, 51, 8, 10, 12, 14, 16, 70, 9, 11, 13, 15, 17, 19, 92, 10, 12, 14, 16, 18, 20, 22, 117, 11, 13, 15, 17, 19, 21, 23, 25, 145, 12, 14, 16, 18, 20, 22, 24, 26, 28</div> <div class=seqdatalinks> (<a href="/A131875/list">list</a>; <a href="/A131875/table">table</a>; <a href="/A131875/graph">graph</a>; <a href="/search?q=A131875+-id:A131875">refs</a>; <a href="/A131875/listen">listen</a>; <a href="/history?seq=A131875">history</a>; <a href="/search?q=id:A131875&fmt=text">text</a>; <a href="/A131875/internal">internal format</a>) </div> </div> </div> <div class=entry> <div class=section> <div class=sectname>OFFSET</div> <div class=sectbody> <div class=sectline>0,2</div> </div> </div> <div class=section> <div class=sectname>COMMENTS</div> <div class=sectbody> <div class=sectline>Left column = pentagonal numbers, <a href="/A000326" title="Pentagonal numbers: a(n) = n*(3*n-1)/2.">A000326</a>: (1, 5, 12, 22, ...).</div> <div class=sectline>Row sums = <a href="/A001106" title="9-gonal (or enneagonal or nonagonal) numbers: a(n) = n*(7*n-5)/2.">A001106</a>: (1, 9, 24, 46, 75, 111, ...).</div> </div> </div> <div class=section> <div class=sectname>LINKS</div> <div class=sectbody> <div class=sectline><a href="/A131875/b131875.txt">Table of n, a(n) for n=0..54.</a></div> </div> </div> <div class=section> <div class=sectname>EXAMPLE</div> <div class=sectbody> <div class=sectline>First few rows of the triangle:</div> <div class=sectline> 1;</div> <div class=sectline> 5, 4;</div> <div class=sectline> 12, 5, 7;</div> <div class=sectline> 22, 6, 8, 10;</div> <div class=sectline> 35, 7, 9, 11, 13;</div> <div class=sectline> 51, 8, 10, 12, 14, 16;</div> <div class=sectline> 70, 9, 11, 13, 15, 17, 19;</div> <div class=sectline> 92, 10, 12, 14, 16, 18, 20, 22;</div> <div class=sectline> ...</div> </div> </div> <div class=section> <div class=sectname>CROSSREFS</div> <div class=sectbody> <div class=sectline>Cf. <a href="/A131844" title="3*A131821 - 2.">A131844</a>, <a href="/A001106" title="9-gonal (or enneagonal or nonagonal) numbers: a(n) = n*(7*n-5)/2.">A001106</a>, <a href="/A000326" title="Pentagonal numbers: a(n) = n*(3*n-1)/2.">A000326</a>.</div> <div class=sectline>Sequence in context: <a href="/A262902" title="a(n) = A049820(A045765(n)); parent-nodes of the leaves of the tree generated by edge-relation A049820(child) = parent.">A262902</a> <a href="/A215332" title="Smooth Lyndon words with 5 colors.">A215332</a> <a href="/A298779" title="Number of nX5 0..1 arrays with every element equal to 0, 3, 4, 5 or 8 king-move adjacent elements, with upper left element zero.">A298779</a> * <a href="/A095871" title="Triangle read by rows: T(n,k)=(n+1)*(3*(n+1)-1)/2-k*(3*k-1)/2">A095871</a> <a href="/A284551" title="Triangular array read by rows, demonstrating that the difference between a pentagonal number (left edge of triangle) and a s...">A284551</a> <a href="/A316671" title="Squares visited by moving diagonally one square on a diagonally numbered board and moving to the lowest available unvisited ...">A316671</a></div> <div class=sectline>Adjacent sequences: <a href="/A131872" title="Set m = 0, n = 1. Find smallest k >= 2 such that pi(k) = (k-pi(k)) - (m-pi(m)); set a(n) = pi(k), m = k, n = n+1. Repeat.">A131872</a> <a href="/A131873" title="Right-to-left partial row sums of triangle A131844">A131873</a> <a href="/A131874" title="a(n) = (7*n^2 + 15*n + 2) / 2.">A131874</a> * <a href="/A131876" title="2*A131873 - 1.">A131876</a> <a href="/A131877" title="a(n) = 14*n + 1.">A131877</a> <a href="/A131878" title="a(n) = 7*n^2 + 14*n + 1.">A131878</a></div> </div> </div> <div class=section> <div class=sectname>KEYWORD</div> <div class=sectbody> <div class=sectline><span title="a sequence of nonnegative numbers">nonn</span>,<span title="typically a triangle of numbers, made into a sequence by reading it row by row"><a href="/A131875/table">tabl</a></span></div> </div> </div> <div class=section> <div class=sectname>AUTHOR</div> <div class=sectbody> <div class=sectline><a href="/wiki/User:Gary_W._Adamson">Gary W. Adamson</a>, Jul 22 2007</div> </div> </div> <div class=section> <div class=sectname>STATUS</div> <div class=sectbody> <div class=sectline>approved</div> </div> </div> </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 April 7 00:47 EDT 2025. Contains 382550 sequences.</div> <div class=legal> <a href="/wiki/Legal_Documents">License Agreements, Terms of Use, Privacy Policy</a> </div> </div> </center> </div> </body> </html>