A167061 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}, {3, 4}}.

40, 47040, 48384000, 49461807360, 50545351901000, 51651393970176000, 52781550346052950760, 53936428658183506928640, 55116575633234676605184000, 56322544581812152703647896000, 57554900528304912551898910864840, 58814220831251084699615165546496000, 60101095479875496770600392870888679560

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}, {3, 4}}. 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) = 1152 a(n-1)

- 138048 a(n-2)

+ 5263416 a(n-3)

- 72792384 a(n-4)

+ 279916416 a(n-5)

- 429599666 a(n-6)

+ 279916416 a(n-7)

- 72792384 a(n-8)

+ 5263416 a(n-9)

- 138048 a(n-10)

+ 1152 a(n-11)

- a(n-12)

G.f.: -40x(x^10 +24x^9 -7104x^8 +167016x^7 -378475x^6 +378475x^4 -167016x^3 +7104x^2 -24x -1)/ (x^12 -1152x^11 +138048x^10 -5263416x^9 +72792384x^8 -279916416x^7 +429599666x^6 -279916416x^5 +72792384x^4 -5263416x^3 +138048x^2 -1152x +1).

Crossrefs

Sequence in context: A185194 A214138 A239168 * A283664 A159404 A323489

Adjacent sequences: A167058 A167059 A167060 * A167062 A167063 A167064

Keyword

nonn

Author

Paul Raff

Status

approved