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A027113 - 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>A027113 - OEIS</title> <link rel="search" type="application/opensearchdescription+xml" title="OEIS" href="/oeis.xml"> <script> var myURL = "\/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=%2fA027113">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="A027113 - 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> A027113 </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). </div> </div> <div class=scorerefs> 32 </div> </div> <div> <div class=seqdatabox> <div class=seqdata>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</div> <div class=seqdatalinks> (<a href="/A027113/list">list</a>; <a href="/A027113/graph">graph</a>; <a href="/search?q=A027113+-id:A027113">refs</a>; <a href="/A027113/listen">listen</a>; <a href="/history?seq=A027113">history</a>; <a href="/search?q=id:A027113&fmt=text">text</a>; <a href="/A027113/internal">internal format</a>) </div> </div> </div> <div class=entry> <div class=section> <div class=sectname>OFFSET</div> <div class=sectbody> <div class=sectline>1,4</div> </div> </div> <div class=section> <div class=sectname>COMMENTS</div> <div class=sectbody> <div class=sectline>The rows are of lengths 1, 3, 5, 7, ...</div> </div> </div> <div class=section> <div class=sectname>LINKS</div> <div class=sectbody> <div class=sectline><a href="/A027113/b027113.txt">Table of n, a(n) for n=1..71.</a></div> </div> </div> <div class=section> <div class=sectname>EXAMPLE</div> <div class=sectbody> <div class=sectline>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; ...</div> </div> </div> <div class=section> <div class=sectname>CROSSREFS</div> <div class=sectbody> <div class=sectline>Sequence in context: <a href="/A356718" title="T(n,k) is the total number of prime factors, counted with multiplicity, of k!*(n-k)!, for 0 <= k <= n. Triangle read by rows.">A356718</a> <a href="/A260931" title="a(n) = A260930(n)/6 for n > 2.">A260931</a> <a href="/A293819" title="Triangle read by rows of the number of integer-sided k-gons having perimeter n, modulo rotations but not reflections, for k=...">A293819</a> * <a href="/A096470" title="Triangle T(n,k), read by rows, formed by setting all entries in the zeroth column and in the main diagonal ((n,n) entries) t...">A096470</a> <a href="/A085143" title="Triangle table from number wall of reversion of Fibonacci numbers.">A085143</a> <a href="/A321029" title="Number of integers x such that 1 <= x <= n and gcd(x,n) = gcd(x+4,n) = gcd(x+6,n) = gcd(x+10,n) = gcd(x+12,n) = 1.">A321029</a></div> <div class=sectline>Adjacent sequences: <a href="/A027110" title="a(n) = Sum_{k=0..2n-1} T(n,k) * T(n,k+1), with T given by A027082.">A027110</a> <a href="/A027111" title="a(n) = Sum_{k=0..2n-2} T(n,k) * T(n,k+2), with T given by A027082.">A027111</a> <a href="/A027112" title="a(n) = Sum_{k=0..2n-3} T(n,k) * T(n,k+3), with T given by A027082.">A027112</a> * <a href="/A027114" title="a(n) = A027113(n, n+2).">A027114</a> <a href="/A027115" title="a(n) = T(n,0) + T(n,1) + ... + T(n,2n), T given by A027113.">A027115</a> <a href="/A027116" title="a(n) = A027113(n, n+3).">A027116</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="an irregular (or funny-shaped) array of numbers made into a sequence by reading it row by row">tabf</span></div> </div> </div> <div class=section> <div class=sectname>AUTHOR</div> <div class=sectbody> <div class=sectline><a href="/wiki/User:Clark_Kimberling">Clark Kimberling</a></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 November 24 08:34 EST 2024. Contains 378054 sequences.</div> <div class=legal> <a href="/wiki/Legal_Documents">License Agreements, Terms of Use, Privacy Policy</a> </div> </div> </center> </div> </body> </html>