A167063 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}}.

21, 16905, 11515392, 7766579625, 5234202655605, 3527304596766720, 2377020102892371573, 1601852459790100499625, 1079473906452564386072064, 727447713589013080159967625, 490220442215546503112745464469, 330355127203424593855513657344000, 222623335689469074506271256084716693

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}, {3, 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) = 805 a(n-1)

- 94300 a(n-2)

+ 4128845 a(n-3)

- 82955561 a(n-4)

+ 801676960 a(n-5)

- 3659544950 a(n-6)

+ 8726681390 a(n-7)

- 11584112776 a(n-8)

+ 8726681390 a(n-9)

- 3659544950 a(n-10)

+ 801676960 a(n-11)

- 82955561 a(n-12)

+ 4128845 a(n-13)

- 94300 a(n-14)

+ 805 a(n-15)

- a(n-16)

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).

Crossrefs

Sequence in context: A220643 A185557 A276513 * A115485 A172724 A001167

Adjacent sequences: A167060 A167061 A167062 * A167064 A167065 A167066

Keyword

nonn,easy

Author

Paul Raff

Status

approved