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A003496 - 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>A003496 - OEIS</title> <link rel="search" type="application/opensearchdescription+xml" title="OEIS" href="/oeis.xml"> <script> var myURL = "\/A003496" 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=%2fA003496">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="A003496 - 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> A003496 </div> <div class=seqname> High temperature series for spherical model internal energy on 3-dimensional simple cubic lattice. <br><font size=-1>(Formerly M4127)</font> </div> </div> <div class=scorerefs> 2 </div> </div> <div> <div class=seqdatabox> <div class=seqdata>1, 6, 18, 132, 810, 5724, 42156, 323352, 2550042, 20559660, 168680196</div> <div class=seqdatalinks> (<a href="/A003496/list">list</a>; <a href="/A003496/graph">graph</a>; <a href="/search?q=A003496+-id:A003496">refs</a>; <a href="/A003496/listen">listen</a>; <a href="/history?seq=A003496">history</a>; <a href="/search?q=id:A003496&fmt=text">text</a>; <a href="/A003496/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>REFERENCES</div> <div class=sectbody> <div class=sectline>G. S. Joyce, Critical properties of the spherical model, in C. Domb and M. S. Green, Phase Transitions and Critical Phenomena, Ac. Press 1972, Vol. 2; see especially pp. 404, 425.</div> <div class=sectline>N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).</div> </div> </div> <div class=section> <div class=sectname>LINKS</div> <div class=sectbody> <div class=sectline><a href="/A003496/b003496.txt">Table of n, a(n) for n=0..10.</a></div> </div> </div> <div class=section> <div class=sectname>CROSSREFS</div> <div class=sectbody> <div class=sectline>Sequence in context: <a href="/A117813" title="Consider 1-D random walk with jumps up to the third neighbor, i.e., set of possible jumps is {-3,-2,-1,+1,+2,+3}. Sequence g...">A117813</a> <a href="/A012758" title="Expansion of e.g.f. arcsin(cosh(x) * log(x+1)).">A012758</a> <a href="/A208822" title="Number of n-bead necklaces labeled with numbers -5..5 allowing reversal, with sum zero.">A208822</a> * <a href="/A009582" title="Expansion of e.g.f.: sinh(log(1+x)/cos(x)).">A009582</a> <a href="/A222913" title="Number of nX2 0..2 arrays with exactly floor(nX2/2) elements equal to at least one horizontal, vertical or antidiagonal neig...">A222913</a> <a href="/A091054" title="Expansion of (1 - 5*x - 2*x^2) / ((1 - x)*(1 + 2*x)*(1 - 6*x)).">A091054</a></div> <div class=sectline>Adjacent sequences: <a href="/A003493" title="High temperature series for spin-1/2 Ising surface susceptibility on square lattice.">A003493</a> <a href="/A003494" title="High temperature series for susceptibility for spherical model on b.c.c. lattice.">A003494</a> <a href="/A003495" title="High temperature series for susceptibility for spherical model on f.c.c. lattice.">A003495</a> * <a href="/A003497" title="Internal energy series for b.c.c. lattice.">A003497</a> <a href="/A003498" title="High temperature series for internal energy for spherical model on f.c.c. lattice.">A003498</a> <a href="/A003499" title="a(n) = 6*a(n-1) - a(n-2), with a(0) = 2, a(1) = 6.">A003499</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="more terms are needed! please extend this sequence">more</span></div> </div> </div> <div class=section> <div class=sectname>AUTHOR</div> <div class=sectbody> <div class=sectline><a href="/wiki/User:N._J._A._Sloane">N. J. A. Sloane</a></div> </div> </div> <div class=section> <div class=sectname>EXTENSIONS</div> <div class=sectbody> <div class=sectline>Better description from <a href="/wiki/User:Steven_Finch">Steven Finch</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 21:55 EST 2024. Contains 378084 sequences.</div> <div class=legal> <a href="/wiki/Legal_Documents">License Agreements, Terms of Use, Privacy Policy</a> </div> </div> </center> </div> </body> </html>