A167066 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}}.

24, 20160, 14515200, 10373448960, 7410329640120, 5293465841664000, 3781306797401609112, 2701118650243184317440, 1929502759140378901785600, 1378310758353447731649144000, 984575190426384431371033497336, 703316214957312006365562863616000, 502403171470887016026721609133115192

Offset: 1

Author

Paul Raff

Keywords

• nonn

References

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

Links

• P. Raff, Table of n, a(n) for n = 1..200
• P. Raff, Spanning Trees in Grid Graphs, arXiv:0809.2551 [math.CO], 2008.
• P. Raff, 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}}. Contains sequence, recurrence, generating function, and more.
• P. Raff, Analysis of the Number of Spanning Trees of Grid Graphs.
• F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Preliminary version of paper that appeared in Ars Combin. 49 (1998), 129-154.
• F. Faase, Counting Hamiltonian cycles in product graphs
• F. Faase, Results from the counting program
• Index entries for sequences related to trees

Formula

a(n) = 840 a(n-1)

- 95522 a(n-2)

+ 4231920 a(n-3)

- 87627601 a(n-4)

+ 863951760 a(n-5)

- 3862082882 a(n-6)

+ 9004563960 a(n-7)

- 11846119204 a(n-8)

+ 9004563960 a(n-9)

- 3862082882 a(n-10)

+ 863951760 a(n-11)

- 87627601 a(n-12)

+ 4231920 a(n-13)

- 95522 a(n-14)

+ 840 a(n-15)

- a(n-16)

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