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A099556 - 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>A099556 - OEIS</title> <link rel="search" type="application/opensearchdescription+xml" title="OEIS" href="/oeis.xml"> <script> var myURL = "\/A099556" 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=%2fA099556">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="A099556 - 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> A099556 </div> <div class=seqname> a(n) = Sum_{k=0..2*n} (n - floor(k/2))^k. </div> </div> <div class=scorerefs> 1 </div> </div> <div> <div class=seqdatabox> <div class=seqdata>1, 2, 5, 18, 91, 604, 5123, 53808, 679389, 10107934, 174544505, 3451802006, 77302457079, 1942469215432, 54339334903015, 1680597906265988, 57116435383949097, 2121725700531106842, 85740960774906267853, 3753239245360442525498, 177284859933198522968819, 9004760569281510790598100</div> <div class=seqdatalinks> (<a href="/A099556/list">list</a>; <a href="/A099556/graph">graph</a>; <a href="/search?q=A099556+-id:A099556">refs</a>; <a href="/A099556/listen">listen</a>; <a href="/history?seq=A099556">history</a>; <a href="/search?q=id:A099556&fmt=text">text</a>; <a href="/A099556/internal">internal format</a>) </div> </div> </div> <div class=entry> <div class=section> <div class=sectname>OFFSET</div> <div class=sectbody> <div class=sectline>1,2</div> </div> </div> <div class=section> <div class=sectname>LINKS</div> <div class=sectbody> <div class=sectline><a href="/A099556/b099556.txt">Table of n, a(n) for n=1..22.</a></div> </div> </div> <div class=section> <div class=sectname>FORMULA</div> <div class=sectbody> <div class=sectline>Row sums of triangle <a href="/A099555" title="Triangle, read by rows, where T(n,k) = (n-floor(k/2))^k for k = 0..2*n - 1, with T(0,0) = 1.">A099555</a>.</div> </div> </div> <div class=section> <div class=sectname>PROG</div> <div class=sectbody> <div class=sectline>(PARI) a(n)=sum(k=0, 2*n, (n-k\2)^k)</div> </div> </div> <div class=section> <div class=sectname>CROSSREFS</div> <div class=sectbody> <div class=sectline>Cf. <a href="/A099555" title="Triangle, read by rows, where T(n,k) = (n-floor(k/2))^k for k = 0..2*n - 1, with T(0,0) = 1.">A099555</a>.</div> <div class=sectline>Sequence in context: <a href="/A113715" title="Row sums of triangle A113711, in which row n forms a polynomial in y=2*k that generates diagonal n as k=0,1,2,... for n>=0.">A113715</a> <a href="/A227094" title="Binomial transform of A013999.">A227094</a> <a href="/A173227" title="Partial sums of A000262.">A173227</a> * <a href="/A057864" title="Number of simple traceable graphs on n nodes.">A057864</a> <a href="/A320154" title="Number of series-reduced balanced rooted trees whose leaves form a set partition of {1,...,n}.">A320154</a> <a href="/A032273" title="Shifts left 2 places under "DIJ" (bracelet, indistinct, labeled) transform.">A032273</a></div> <div class=sectline>Adjacent sequences: <a href="/A099553" title="Number of rooted 2-connected loopless 4-regular planar maps with n inner faces.">A099553</a> <a href="/A099554" title="Decimal expansion of the constant x that satisfies x = exp(1/sqrt(x)).">A099554</a> <a href="/A099555" title="Triangle, read by rows, where T(n,k) = (n-floor(k/2))^k for k = 0..2*n - 1, with T(0,0) = 1.">A099555</a> * <a href="/A099557" title="Slanted Pascal's triangle, read by rows, such that T(n,k) = binomial(n-[k/2],k) for [n*2/3]>=k>=0, where [x]=floor(x).">A099557</a> <a href="/A099558" title="Antidiagonal sums of the triangle A099557.">A099558</a> <a href="/A099559" title="a(n) = Sum_{k=0..floor(n/5)} C(n-4k,k+1).">A099559</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="it is very easy to produce terms of sequence">easy</span></div> </div> </div> <div class=section> <div class=sectname>AUTHOR</div> <div class=sectbody> <div class=sectline><a href="/wiki/User:Paul_D._Hanna">Paul D. Hanna</a>, Oct 22 2004</div> </div> </div> <div class=section> <div class=sectname>EXTENSIONS</div> <div class=sectbody> <div class=sectline>a(13) and following terms from <a href="/wiki/User:Georg_Fischer">Georg Fischer</a>, Nov 21 2024</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 March 13 19:40 EDT 2025. Contains 381739 sequences.</div> <div class=legal> <a href="/wiki/Legal_Documents">License Agreements, Terms of Use, Privacy Policy</a> </div> </div> </center> </div> </body> </html>