Search: id:A003761
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%I A003761
%S A003761 3,270,20160,1477980,108097935,7903526400,577834413429,
%T A003761 42245731959480,3088601154192960,225808743709815750,
%U A003761 16508958287605688193,1206975861055570636800
%N A003761 Number of spanning trees in D_4 X P_n.
%D A003761 F. Faase, On the number of specific spanning subgraphs of the graphs 
               G X P_n, Ars Combin. 49 (1998), 129-154.
%H A003761 F. Faase, <a href="http://www.iwriteiam.nl/Cpaper.zip">On the number 
               of specific spanning subgraphs of the graphs G X P_n</a>, Preliminary 
               version of paper that appeared in Ars Combin. 49 (1998), 129-154.
%H A003761 F. Faase, <a href="http://www.iwriteiam.nl/counting.html">Counting Hamilton 
               cycles in product graphs</a>
%H A003761 F. Faase, <a href="http://www.iwriteiam.nl/Cresults.html">Results from 
               the counting program</a>
%H A003761 F. Faase, <a href="http://home.wxs.nl/~faase009/counting.html">Counting 
               Hamilton cycles in product graphs</a>
%H A003761 <a href="Sindx_Tra.html#trees">Index entries for sequences related to 
               trees</a>
%H A003761 P. Raff, <a href="http://arxiv.org/abs/0809.2551">Spanning Trees in Grid 
               Graphs</a>. [From Paul Raff (praff(AT)math.rutgers.edu), Mar 06 2009]
%H A003761 P. Raff, <a href="http://www.math.rutgers.edu/~praff/span/4/12-13-14-23/
               index.xml">Analysis of the Number of Spanning Trees of D_4 x P_n</
               a>. Contains sequence, recurrence, generating function, and more. 
               [From Paul Raff (praff(AT)math.rutgers.edu), Mar 06 2009]
%F A003761 a(1) = 3,
%F A003761 a(2) = 270,
%F A003761 a(3) = 20160,
%F A003761 a(4) = 1477980,
%F A003761 a(5) = 108097935,
%F A003761 a(6) = 7903526400,
%F A003761 a(7) = 577834413429,
%F A003761 a(8) = 42245731959480 and
%F A003761 a(n) = 90a(n-1) - 1313a(n-2) + 5850a(n-3) - 9828a(n-4) + 5850a(n-5) - 
               1313a(n-6) + 90a(n-7) - a(n-8).
%F A003761 G.f.: 3x(x^6-67x^4+180x^3-67x^2+1)/(x^8-90x^7+1313x^6-5850x^5+9828x^4-5850x^3+1313x^2-90x+1) 
               [From Paul Raff (praff(AT)math.rutgers.edu), Mar 06 2009]
%F A003761 a(n)=3*A006238(n)*A001109(n). [R. Guy, seqfan list, Mar 28 2009] [From 
               R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 03 2009]
%Y A003761 Sequence in context: A051490 A003381 A058451 this_sequence A105318 A115477 
               A051365
%Y A003761 Adjacent sequences: A003758 A003759 A003760 this_sequence A003762 A003763 
               A003764
%K A003761 nonn
%O A003761 1,1
%A A003761 Frans Faase (Frans_LiXia(AT)wxs.nl)
%E A003761 Added recurrence from Faase's web page. - N. J. A. Sloane (njas(AT)research.att.com), 
               Feb 03 2009

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