%I #16 Aug 23 2023 10:18:29

%S 3,969,232551,53799849,12372096000,2842087396401,652745210821239,

%T 149910861311886393,34428589607251552779,7906872302105745408000,

%U 1815892322798648692785531,417037814066206883492561817,95776899454583611992923575575,21996121549640772495096513751713

%N Number of spanning trees in G X P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 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="/A167067/b167067.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/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}}.</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) = 323 a(n-1)

%F - 24404 a(n-2)

%F + 723520 a(n-3)

%F - 9950948 a(n-4)

%F + 71523505 a(n-5)

%F - 283937931 a(n-6)

%F + 637842312 a(n-7)

%F - 832457728 a(n-8)

%F + 637842312 a(n-9)

%F - 283937931 a(n-10)

%F + 71523505 a(n-11)

%F - 9950948 a(n-12)

%F + 723520 a(n-13)

%F - 24404 a(n-14)

%F + 323 a(n-15)

%F - a(n-16).

%F G.f.: -3x (x^14 -2408x^12 +54264x^11 -439553x^10 +1500658x^9 -1911656x^8 +1911656x^6 -1500658x^5 +439553x^4 -54264x^3 +2408x^2 -1)/(x^16 -323x^15 +24404x^14 -723520x^13 +9950948x^12 -71523505x^11 +283937931x^10 -637842312x^9 +832457728x^8 -637842312x^7 +283937931x^6 -71523505x^5 +9950948x^4 -723520x^3 +24404x^2 -323x+1).

%K nonn

%O 1,1

%A _Paul Raff_