%I #14 Aug 23 2023 10:17:56

%S 11,6061,2733511,1215842661,540144000000,239933520731861,

%T 106577890632874111,47341582784338831461,21028987835540967334811,

%U 9341012640240002304000000,4149249488236281570533713211,1843084039808720108847180812661,818692341198182161542031245824911

%N Number of spanning trees in G X P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 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="/A167068/b167068.txt">Table of n, a(n) for n = 1..200</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/5/12-13-14-23-25-45/index.xml">Analysis of the Number of Spanning Trees of G x P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 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 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 <a href="/index/Tra#trees">Index entries for sequences related to trees</a>

%F a(n) = 551 a(n-1)

%F - 51500 a(n-2)

%F + 1873400 a(n-3)

%F - 31993500 a(n-4)

%F + 271314053 a(n-5)

%F - 1157139603 a(n-6)

%F + 2669595000 a(n-7)

%F - 3507446800 a(n-8)

%F + 2669595000 a(n-9)

%F - 1157139603 a(n-10)

%F + 271314053 a(n-11)

%F - 31993500 a(n-12)

%F + 1873400 a(n-13)

%F - 51500 a(n-14)

%F + 551 a(n-15)

%F - a(n-16)

%F G.f.: -11x (x^14 -3600x^12 +110200x^11 -1112601x^10 +3855898x^9 -4841800x^8 +4841800x^6 -3855898x^5 +1112601x^4 -110200x^3 +3600x^2-1)/(x^16 -551x^15 +51500x^14 -1873400x^13 +31993500x^12 -271314053x^11 +1157139603x^10 -2669595000x^9 +3507446800x^8 -2669595000x^7 +1157139603x^6 -271314053x^5 +31993500x^4 -1873400x^3 +51500x^2 -551x+1).

%K nonn

%O 1,1

%A _Paul Raff_