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A002910 - 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>A002910 - OEIS</title> <link rel="search" type="application/opensearchdescription+xml" title="OEIS" href="/oeis.xml"> <script> var myURL = "\/A002910" 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=%2fA002910">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="A002910 - 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> A002910 </div> <div class=seqname> High-temperature series in v = tanh(J/kT) for susceptibility for the Ising model on honeycomb structure. <br><font size=-1>(Formerly M2558 N1012)</font> </div> </div> <div class=scorerefs> 5 </div> </div> <div> <div class=seqdatabox> <div class=seqdata>1, 3, 6, 12, 24, 48, 90, 168, 318, 600, 1098, 2004, 3696, 6792, 12270, 22140, 40224, 72888, 130650, 234012, 421176, 756624, 1348998, 2403840, 4299018, 7677840, 13635630, 24206220, 43092888, 76635984, 135698970, 240199320, 426144654, 755420328, 1334488074</div> <div class=seqdatalinks> (<a href="/A002910/list">list</a>; <a href="/A002910/graph">graph</a>; <a href="/search?q=A002910+-id:A002910">refs</a>; <a href="/A002910/listen">listen</a>; <a href="/history?seq=A002910">history</a>; <a href="/search?q=id:A002910&fmt=text">text</a>; <a href="/A002910/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>Previous name was: Susceptibility series for honeycomb.</div> </div> </div> <div class=section> <div class=sectname>REFERENCES</div> <div class=sectbody> <div class=sectline>C. Domb, Ising model, in Phase Transitions and Critical Phenomena, vol. 3, ed. C. Domb and M. S. Green, Academic Press, 1974; p. 380.</div> <div class=sectline>N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).</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="/A002910/b002910.txt">Table of n, a(n) for n=0..34.</a></div> <div class=sectline>Y. Chan, A. J. Guttmann, B. G. Nickel, J. H. H. Perk, <a href="https://doi.org/10.1007/s10955-011-0212-0">The Ising Susceptibility Scaling Function</a>, J Stat Phys 145 (2011), 549-590; arXiv:<a href="https://arxiv.org/abs/1012.5272">1012.5272</a> [cond-mat.stat-mech], 2010-2020. Gives 639 terms in the file Honeycomb_v638.txt.</div> <div class=sectline>C. Domb, <a href="/A007239/a007239.pdf">Ising model</a>, Phase Transitions and Critical Phenomena 3 (1974), 257, 380-381, 384-387, 390-391, 412-423. (Annotated scanned copy)</div> <div class=sectline>M. F. Sykes, <a href="https://doi.org/10.1063/1.1724212">Some counting theorems in the theory of the Ising problem and the excluded volume problem</a>, J. Math. Phys., 2 (1961), 52-62.</div> <div class=sectline>M. F. Sykes and M. E. Fisher, <a href="https://doi.org/10.1016/0031-8914(62)90080-0">Antiferromagnetic susceptibility of the plane square and honeycomb Ising lattices</a>, Physica, 28 (1962), 919-938.</div> <div class=sectline>M. F. Sykes, D. G. Gaunt, P. D. Roberts and J. A. Wyles, <a href="https://doi.org/10.1088/0305-4470/5/5/004">High temperature series for the susceptibility of the Ising model, I. Two dimensional lattices</a>, J. Phys. A 5 (1972) 624-639.</div> </div> </div> <div class=section> <div class=sectname>CROSSREFS</div> <div class=sectbody> <div class=sectline>Cf. <a href="/A002978" title="Low-temperature series in y = exp(2J/kT) for antiferromagnetic susceptibility for the Ising model on honeycomb structure.">A002978</a>.</div> <div class=sectline>Sequence in context: <a href="/A322676" title="Numbers k > 0 such that k has more divisors d, such that d-1 is prime, than any other smaller positive number, with a(1) = 1.">A322676</a> <a href="/A102255" title="Slowest increasing sequence beginning with 3 whose digits satisfy the rule d*2.">A102255</a> <a href="/A192871" title="Number of n-step prudent self-avoiding walks on honeycomb lattice.">A192871</a> * <a href="/A001668" title="Number of self-avoiding n-step walks on honeycomb lattice.">A001668</a> <a href="/A080616" title="Consider 3 X 3 X 3 Rubik cube, but only allow the moves T2, F2, R2; sequence gives number of positions that are exactly n mo...">A080616</a> <a href="/A090572" title="Number of configurations of the 3-dimensional 2 X 2 X 2 sliding cube puzzle that require a minimum of n moves to be reached.">A090572</a></div> <div class=sectline>Adjacent sequences: <a href="/A002907" title="High temperature series in v = tanh(J/kT) for residual correlation function (correction to susceptibility) for the spin-1/2 ...">A002907</a> <a href="/A002908" title="High temperature expansion of -u/J in odd powers of v = tanh(J/kT), where u is energy per site of the spin-1/2 Ising model o...">A002908</a> <a href="/A002909" title="Low temperature energy function for square lattice.">A002909</a> * <a href="/A002911" title="Erroneous version of A047709.">A002911</a> <a href="/A002912" title="Low-temperature series in z = exp(-2J/kT) for ferromagnetic susceptibility for the Ising model on honeycomb structure.">A002912</a> <a href="/A002913" title="High temperature series for spin-1/2 Ising magnetic susceptibility on 3-dimensional simple cubic lattice.">A002913</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 exceptionally nice sequence">nice</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>New name and more terms from Chan et al added by <a href="/wiki/User:Andrey_Zabolotskiy">Andrey Zabolotskiy</a>, Mar 03 2021</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 02:23 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>