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Number of spanning trees in G X P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {2, 5}, {3, 5}, {4, 5}}.
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%I #12 Aug 23 2023 10:18:11

%S 12,6720,3110400,1423806720,651286330860,297900675072000,

%T 136260356109480876,62325740425973498880,28507909150300692211200,

%U 13039570449847302883368000,5964323676112090939594326348,2728092696767010687412666368000,1247834652562251646622689145644236

%N Number of spanning trees in G X P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {2, 5}, {3, 5}, {4, 5}}.

%D F. Faase, On the number of specific spanning subgraphs of the graphs A X P_n, Ars Combin. 49 (1998), 129-154.

%H P. Raff, <a href="/A167072/b167072.txt">Table of n, a(n) for n = 1..200</a>

%H 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 F. Faase, <a href="http://www.iwriteiam.nl/counting.html">Counting Hamiltonian cycles in product graphs</a>

%H F. Faase, <a href="http://www.iwriteiam.nl/Cresults.html">Results from the counting program</a>

%H P. Raff, <a href="http://arxiv.org/abs/0809.2551">Spanning Trees in Grid Graphs</a>, arXiv:0809.2551 [math.CO], 2008.

%H P. Raff, <a href="http://www.math.rutgers.edu/~praff/span/5/12-13-14-25-35-45/index.xml">Analysis of the Number of Spanning Trees of G x P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {2, 5}, {3, 5}, {4, 5}}.</a> Contains sequence, recurrence, generating function, and more.

%H 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 <a href="/index/Tra#trees">Index entries for sequences related to trees</a>

%F a(n) = 525 a(n-1)

%F - 32415 a(n-2)

%F + 696920 a(n-3)

%F - 5936265 a(n-4)

%F + 19827675 a(n-5)

%F - 29313582 a(n-6)

%F + 19827675 a(n-7)

%F - 5936265 a(n-8)

%F + 696920 a(n-9)

%F - 32415 a(n-10)

%F + 525 a(n-11)

%F - a(n-12).

%F G.f.: -12x (x^10 +35x^9 -2385x^8 +26040x^7 -54030x^6 +54030x^4 -26040x^3 +2385x^2 -35x-1) / (x^12 -525x^11 +32415x^10 -696920x^9 +5936265x^8 -19827675x^7 +29313582x^6 -19827675x^5 +5936265x^4 -696920x^3 +32415x^2 -525x+1).

%K nonn

%O 1,1

%A _Paul Raff_, Jun 01 2010