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A003200 - 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>A003200 - OEIS</title> <link rel="search" type="application/opensearchdescription+xml" title="OEIS" href="/oeis.xml"> <script> var myURL = "\/A003200" 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=%2fA003200">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="A003200 - 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> A003200 </div> <div class=seqname> Cluster series for site percolation problem on honeycomb matching lattice (honeycomb structure with 1st, 2nd and 3rd neighbors connected). <br><font size=-1>(Formerly M4848)</font> </div> </div> <div class=scorerefs> 11 </div> </div> <div> <div class=seqdatabox> <div class=seqdata>1, 12, 66, 312, 1368, 5685, 23034, 90288, 350124</div> <div class=seqdatalinks> (<a href="/A003200/list">list</a>; <a href="/A003200/graph">graph</a>; <a href="/search?q=A003200+-id:A003200">refs</a>; <a href="/A003200/listen">listen</a>; <a href="/history?seq=A003200">history</a>; <a href="/search?q=id:A003200&fmt=text">text</a>; <a href="/A003200/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>J. W. Essam, Percolation and cluster size, in C. Domb and M. S. Green, Phase Transitions and Critical Phenomena, Ac. Press 1972, Vol. 2; see especially pp. 225-226.</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="/A003200/b003200.txt">Table of n, a(n) for n=0..8.</a></div> <div class=sectline>Keith Malcolm Gwilym, <a href="https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.704220">Theory of percolation processes</a>, PhD Thesis, University of London, 1972. See Table 3.1 on p. 55.</div> <div class=sectline>M. F. Sykes and J. W. Essam, <a href="https://doi.org/10.1103/PhysRev.133.A310">Critical percolation probabilities by series methods</a>, Phys. Rev., 133 (1964), A310-A315.</div> </div> </div> <div class=section> <div class=sectname>CROSSREFS</div> <div class=sectbody> <div class=sectline>Cf. cluster series for site percolation problem: <a href="/A003201" title="Cluster series for site percolation problem on square matching lattice (square lattice with 1st and 2nd neighbors connected).">A003201</a>, <a href="/A003202" title="Cluster series for hexagonal lattice.">A003202</a>, <a href="/A003203" title="Cluster series for square lattice.">A003203</a>, <a href="/A003204" title="Cluster series for honeycomb.">A003204</a>, <a href="/A003209" title="Cluster series for f.c.c. lattice.">A003209</a>, <a href="/A003210" title="Cluster series for b.c.c. lattice.">A003210</a>, <a href="/A003211" title="Cluster series for cubic lattice.">A003211</a>, <a href="/A003212" title="Cluster series for diamond.">A003212</a>, <a href="/A036392" title="Coefficients of cluster series for site percolation problem on triangular lattice with 1st and 2nd neighbor bonds.">A036392</a>, <a href="/A036394" title="Coefficients of cluster series for site percolation problem on f.c.c. lattice with 1st and 2nd neighbor bonds.">A036394</a>, <a href="/A036395" title="Coefficients of cluster series for site percolation problem on b.c.c. lattice with 1st and 2nd neighbor bonds.">A036395</a>, <a href="/A036396" title="Coefficients of cluster series for site percolation problem on simple cubic lattice with 1st and 2nd neighbor bonds.">A036396</a>, <a href="/A036397" title="Coefficients of cluster series for site percolation problem on triangular lattice with 1st, 2nd and 3rd neighbor bonds.">A036397</a>, <a href="/A036398" title="Coefficients of cluster series for site percolation problem on square lattice with 1st, 2nd and 3rd neighbor bonds.">A036398</a>, <a href="/A036400" title="Coefficients of cluster series for site percolation problem on f.c.c. lattice with 1st, 2nd and 3rd neighbor bonds.">A036400</a>, <a href="/A036401" title="Coefficients of cluster series for site percolation problem on b.c.c. lattice with 1st, 2nd and 3rd neighbor bonds.">A036401</a>, <a href="/A036402" title="Coefficients of cluster series for site percolation problem on simple cubic lattice with 1st, 2nd and 3rd neighbor bonds.">A036402</a> and for bond percolation problem: <a href="/A003197" title="Cluster series for bond percolation problem on hexagonal lattice.">A003197</a>, <a href="/A003198" title="Cluster series for bond percolation problem on square lattice.">A003198</a>, <a href="/A003199" title="Cluster series for bond percolation problem on honeycomb.">A003199</a>, <a href="/A003205" title="Cluster series for bond percolation problem on f.c.c. lattice.">A003205</a>, <a href="/A003206" title="Cluster series for bond percolation problem on b.c.c. lattice.">A003206</a>, <a href="/A003207" title="Cluster series for bond percolation problem on cubic lattice.">A003207</a>, <a href="/A003208" title="Cluster series for bond percolation problem on diamond.">A003208</a>.</div> <div class=sectline>Sequence in context: <a href="/A180392" title="Number of permutations of 1..n with both permutation and its inverse having exactly 2 maxima">A180392</a> <a href="/A161805" title="A trisection of A161804: a(n) = A161804(3n) for n>=0.">A161805</a> <a href="/A036399" title="Duplicate of A003200.">A036399</a> * <a href="/A353291" title="Integers whose cube is the sum of the cubes of four primes, not necessarily distinct.">A353291</a> <a href="/A200190" title="Number of -6..6 arrays x(0..n-1) of n elements with zero sum, adjacent elements differing by more than one, and elements alt...">A200190</a> <a href="/A270251" title="Number of nXnXn triangular 0..2 arrays with some element plus some adjacent element totalling 2 exactly once.">A270251</a></div> <div class=sectline>Adjacent sequences: <a href="/A003197" title="Cluster series for bond percolation problem on hexagonal lattice.">A003197</a> <a href="/A003198" title="Cluster series for bond percolation problem on square lattice.">A003198</a> <a href="/A003199" title="Cluster series for bond percolation problem on honeycomb.">A003199</a> * <a href="/A003201" title="Cluster series for site percolation problem on square matching lattice (square lattice with 1st and 2nd neighbors connected).">A003201</a> <a href="/A003202" title="Cluster series for hexagonal lattice.">A003202</a> <a href="/A003203" title="Cluster series for square lattice.">A003203</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>Name clarified by <a href="/wiki/User:Andrey_Zabolotskiy">Andrey Zabolotskiy</a>, Mar 04 2021</div> <div class=sectline>a(6)-a(8) from Gwilym added by <a href="/wiki/User:Andrey_Zabolotskiy">Andrey Zabolotskiy</a>, Apr 13 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 December 3 16:59 EST 2024. Contains 378391 sequences.</div> <div class=legal> <a href="/wiki/Legal_Documents">License Agreements, Terms of Use, Privacy Policy</a> </div> </div> </center> </div> </body> </html>