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A003498 - 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>A003498 - OEIS</title> <link rel="search" type="application/opensearchdescription+xml" title="OEIS" href="/oeis.xml"> <script> var myURL = "\/A003498" 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=%2fA003498">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="A003498 - 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> A003498 </div> <div class=seqname> High temperature series for internal energy for spherical model on f.c.c. lattice. <br><font size=-1>(Formerly M4839)</font> </div> </div> <div class=scorerefs> 1 </div> </div> <div> <div class=seqdatabox> <div class=seqdata>1, 12, 48, 252, 1440, 8544, 52416, 330588, 2130240, 13961808, 92784384, 623772288, 4234688640, 28990262016, 199908428544, 1387276513308, 9681052037760, 67895140257840, 478281284627328, 3382695596455344</div> <div class=seqdatalinks> (<a href="/A003498/list">list</a>; <a href="/A003498/graph">graph</a>; <a href="/search?q=A003498+-id:A003498">refs</a>; <a href="/A003498/listen">listen</a>; <a href="/history?seq=A003498">history</a>; <a href="/search?q=id:A003498&fmt=text">text</a>; <a href="/A003498/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="/A003498/b003498.txt">Table of n, a(n) for n=0..19.</a></div> <div class=sectline><a href="/index/Fa#fcc">Index entries for sequences related to f.c.c. lattice</a></div> </div> </div> <div class=section> <div class=sectname>CROSSREFS</div> <div class=sectbody> <div class=sectline>Cf. <a href="/A047712" title="High-temperature coefficients for internal energy for spin-1/2 Ising model on f.c.c. lattice.">A047712</a> (Ising model), <a href="/A003495" title="High temperature series for susceptibility for spherical model on f.c.c. lattice.">A003495</a> (susceptibility), <a href="/A003496" title="High temperature series for spherical model internal energy on 3-dimensional simple cubic lattice.">A003496</a> (cubic lattice), <a href="/A003497" title="Internal energy series for b.c.c. lattice.">A003497</a> (b.c.c. lattice).</div> <div class=sectline>Sequence in context: <a href="/A242026" title="Number of non-palindromic n-tuples of 4 distinct elements.">A242026</a> <a href="/A340727" title="a(n) is the smallest integer that can be written as a product of n distinct integers > 1 in at least two different ways.">A340727</a> <a href="/A052601" title="E.g.f. (1-x)/(1-x-2x^3).">A052601</a> * <a href="/A326743" title="Number of length n self-avoiding walks on the kisrhombille tiling starting at a degree 12 vertex.">A326743</a> <a href="/A269030" title="Number of n X 3 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalli...">A269030</a> <a href="/A222359" title="Number of nX7 0..1 arrays with no more than floor(nX7/2) elements unequal to at least one king-move neighbor, with new value...">A222359</a></div> <div class=sectline>Adjacent sequences: <a href="/A003495" title="High temperature series for susceptibility for spherical model on f.c.c. lattice.">A003495</a> <a href="/A003496" title="High temperature series for spherical model internal energy on 3-dimensional simple cubic lattice.">A003496</a> <a href="/A003497" title="Internal energy series for b.c.c. lattice.">A003497</a> * <a href="/A003499" title="a(n) = 6*a(n-1) - a(n-2), with a(0) = 2, a(1) = 6.">A003499</a> <a href="/A003500" title="a(n) = 4*a(n-1) - a(n-2) with a(0) = 2, a(1) = 4.">A003500</a> <a href="/A003501" title="a(n) = 5*a(n-1) - a(n-2), with a(0) = 2, a(1) = 5.">A003501</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>a(16)-a(19) from Joyce added and name clarified by <a href="/wiki/User:Andrey_Zabolotskiy">Andrey Zabolotskiy</a>, Oct 18 2023</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 20:35 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>