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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> <div class="motdbox"> <div class="motd"> <p>Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).</p> </div> <div class="donate"> <div id="donate-button-container"> <div id="donate-button"></div> <script src="https://www.paypalobjects.com/donate/sdk/donate-sdk.js" charset="UTF-8"></script> <script> PayPal.Donation.Button({ env:'production', hosted_button_id:'SVPGSDDCJ734A', image: { src:'https://www.paypalobjects.com/en_US/i/btn/btn_donateCC_LG.gif', alt:'Donate with PayPal button', title:'PayPal - The safer, easier way to pay online!', } }).render('#donate-button'); </script> </div> <a href="https://oeisf.org/donate/"> <strong>Other ways to Give</strong> </a> </div> </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 December 3 16:59 EST 2024. 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