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

%I #17 Aug 23 2023 10:18:04

%S 21,16905,11515392,7766579625,5234202655605,3527304596766720,

%T 2377020102892371573,1601852459790100499625,1079473906452564386072064,

%U 727447713589013080159967625,490220442215546503112745464469,330355127203424593855513657344000,222623335689469074506271256084716693

%N Number of spanning trees in G X P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {1, 5}, {2, 3}, {2, 4}, {3, 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="/A167063/b167063.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/5/12-13-14-15-23-24-35/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}, {3, 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) = 805 a(n-1)

%F - 94300 a(n-2)

%F + 4128845 a(n-3)

%F - 82955561 a(n-4)

%F + 801676960 a(n-5)

%F - 3659544950 a(n-6)

%F + 8726681390 a(n-7)

%F - 11584112776 a(n-8)

%F + 8726681390 a(n-9)

%F - 3659544950 a(n-10)

%F + 801676960 a(n-11)

%F - 82955561 a(n-12)

%F + 4128845 a(n-13)

%F - 94300 a(n-14)

%F + 805 a(n-15)

%F - a(n-16)

%F G.f.: -21x(x^14 -5373x^12 +196420x^11 -2311184x^10 +8452500x^9 -10863790x^8 +10863790x^6 -8452500x^5 +2311184x^4 -196420x^3 +5373x^2 -1)/ (x^16 -805x^15 +94300x^14 -4128845x^13 +82955561x^12 -801676960x^11 +3659544950x^10 -8726681390x^9 +11584112776x^8 -8726681390x^7 +3659544950x^6 -801676960x^5 +82955561x^4 -4128845x^3 +94300x^2 -805x +1).

%K nonn,easy

%O 1,1

%A _Paul Raff_