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

%I #12 Aug 23 2023 10:18:00

%S 24,20160,14515200,10373448960,7410329640120,5293465841664000,

%T 3781306797401609112,2701118650243184317440,1929502759140378901785600,

%U 1378310758353447731649144000,984575190426384431371033497336,703316214957312006365562863616000,502403171470887016026721609133115192

%N Number of spanning trees in G X P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {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="/A167066/b167066.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/5/12-13-14-23-24-35-45/index.xml">Analysis of the Number of Spanning Trees of G x P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {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 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) = 840 a(n-1)

%F - 95522 a(n-2)

%F + 4231920 a(n-3)

%F - 87627601 a(n-4)

%F + 863951760 a(n-5)

%F - 3862082882 a(n-6)

%F + 9004563960 a(n-7)

%F - 11846119204 a(n-8)

%F + 9004563960 a(n-9)

%F - 3862082882 a(n-10)

%F + 863951760 a(n-11)

%F - 87627601 a(n-12)

%F + 4231920 a(n-13)

%F - 95522 a(n-14)

%F + 840 a(n-15)

%F - a(n-16)

%F G.f.: -24x(x^14 -5278x^12 +201600x^11 -2458194x^10 +8663760x^9 -10786195x^8 +10786195x^6 -8663760x^5 +2458194x^4 -201600x^3 +5278x^2 -1)/ (x^16 -840x^15 +95522x^14 -4231920x^13 +87627601x^12 -863951760x^11 +3862082882x^10 -9004563960x^9 +11846119204x^8 -9004563960x^7 +3862082882x^6 -863951760x^5 +87627601x^4 -4231920x^3 +95522x^2 -840x +1).

%K nonn

%O 1,1

%A _Paul Raff_