A167060 Number of spanning trees in G X P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {1, 5}, {2, 3}, {2, 4}, {2, 5}}

20, 15680, 10368000, 6788875520, 4442379540500, 2906788405248000, 1901996646002328980, 1244531724569497441280, 814333290473214499968000, 532841946954369840453512000, 348653977101113682528774921620, 228134433564164121977905348608000, 149274992387437573877742622270584980

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}, {2, 4}, {2, 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) = 720 a(n-1)

- 43920 a(n-2)

+ 624783 a(n-3)

- 2247840 a(n-4)

+ 2247840 a(n-5)

- 624783 a(n-6)

+ 43920 a(n-7)

- 720 a(n-8)

+ a(n-9)

G.f.: -20x(x^7 +64x^6 -2160x^5 +4273x^4 +4273x^3 -2160x^2 +64x +1)/ (x^9 -720x^8 +43920x^7 -624783x^6 +2247840x^5 -2247840x^4 +624783x^3 -43920x^2 +720x -1).

Crossrefs

Sequence in context: A173790 A028667 A201507 * A172661 A172758 A146497

Adjacent sequences: A167057 A167058 A167059 * A167061 A167062 A167063

Keyword

nonn

Author

Paul Raff

Status

approved