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%I A167059 #14 Aug 23 2023 09:44:13
%S A167059 8,4032,1612800,631427328,246562692200,96244833484800,
%T A167059 37566939748080392,14663279200231130112,5723424260979717196800,
%U A167059 2233987356983360324068800,871977888467614764819315368,340353508793721676084268236800,132847991246505889127220947758952
%N A167059 Number of spanning trees in G X P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {1, 5}, {2, 3}, {2, 4}}.
%D A167059 F. Faase, On the number of specific spanning subgraphs of the graphs A X P_n, Ars Combin. 49 (1998), 129-154.
%H A167059 P. Raff, <a href="/A167059/b167059.txt">Table of n, a(n) for n = 1..200</a>
%H A167059 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 A167059 F. Faase, <a href="http://www.iwriteiam.nl/counting.html">Counting Hamiltonian cycles in product graphs</a>
%H A167059 F. Faase, <a href="http://www.iwriteiam.nl/Cresults.html">Results from the counting program</a>
%H A167059 P. Raff, <a href="http://arxiv.org/abs/0809.2551">Spanning Trees in Grid Graphs</a>, arXiv:0809.2551 [math.CO], 2008.
%H A167059 P. Raff, <a href="http://www.math.rutgers.edu/~praff/span/5/12-13-14-15-23-24/index.xml">Analysis of the Number of Spanning Trees of G x P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {1, 5}, {2, 3}, {2, 4}}.</a> Contains sequence, recurrence, generating function, and more.
%H A167059 P. Raff, <a href="http://www.myraff.com/projects/spanning-trees-in-grid-graphs">Analysis of the Number of Spanning Trees of Grid Graphs</a>.
%H A167059 <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%F A167059 a(n) = 504 a(n-1)
%F A167059 - 48706 a(n-2)
%F A167059 + 1765008 a(n-3)
%F A167059 - 29021617 a(n-4)
%F A167059 + 239655024 a(n-5)
%F A167059 - 1039298722 a(n-6)
%F A167059 + 2447629128 a(n-7)
%F A167059 - 3242171236 a(n-8)
%F A167059 + 2447629128 a(n-9)
%F A167059 - 1039298722 a(n-10)
%F A167059 + 239655024 a(n-11)
%F A167059 - 29021617 a(n-12)
%F A167059 + 1765008 a(n-13)
%F A167059 - 48706 a(n-14)
%F A167059 + 504 a(n-15)
%F A167059 - a(n-16)
%F A167059 G.f.: -8x (x^14 -3710x^12 +104832x^11 -997954x^10 +3633840x^9 -4759203x^8 +4759203x^6 -3633840x^5 +997954x^4 -104832x^3 +3710x^2-1)/ (x^16 -504x^15 +48706x^14 -1765008x^13 +29021617x^12 -239655024x^11 +1039298722x^10 -2447629128x^9 +3242171236x^8 -2447629128x^7 +1039298722x^6 -239655024x^5 +29021617x^4 -1765008x^3 +48706x^2 -504x+1).
%K A167059 nonn
%O A167059 1,1
%A A167059 _Paul Raff_, Jun 01 2010

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