A167064 Number of spanning trees in G X P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {1, 5}, {2, 3}, {4, 5}}.

9, 4725, 1990656, 822343725, 338887026225, 139607890329600, 57510072475569441, 23690531503846057725, 9758998421421748936704, 4020088612537397612953125, 1656021591727120808594862489, 682175884126257323680569753600, 281013205982204002882115759532921

Offset

1,1

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

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

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}, {1, 5}, {2, 3}, {4, 5}}. Contains sequence, recurrence, generating function, and more.

P. Raff, Analysis of the Number of Spanning Trees of Grid Graphs.

Index entries for sequences related to trees

Formula

a(n) = 504 a(n-1)

- 40152 a(n-2)

+ 937188 a(n-3)

- 8104008 a(n-4)

+ 27431208 a(n-5)

- 40609478 a(n-6)

+ 27431208 a(n-7)

- 8104008 a(n-8)

+ 937188 a(n-9)

- 40152 a(n-10)

+ 504 a(n-11)

- a(n-12)

G.f.: -9x(x^10 +21x^9 -3264x^8 +37401x^7 -74299x^6 +74299x^4 -37401x^3 +3264x^2 -21x -1)/ (x^12 -504x^11 +40152x^10 -937188x^9 +8104008x^8 -27431208x^7 +40609478x^6 -27431208x^5 +8104008x^4 -937188x^3 +40152x^2 -504x +1).

Crossrefs

Sequence in context: A193310 A216421 A323337 * A125541 A151581 A145263

Adjacent sequences: A167061 A167062 A167063 * A167065 A167066 A167067

Keyword

nonn

Author

Paul Raff

Status

approved