A003767 Number of spanning trees in (K_4 - e) X P_n.

8, 1152, 147000, 18643968, 2363741512, 299675376000, 37992808932728, 4816723274883072, 610663532419269000, 77419840899743388288, 9815277065807118267832, 1244379512520754017408000

Offset

1,1

References

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

Links

Table of n, a(n) for n=1..12.

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 (K_4 - e) x P_n. Contains sequence, recurrence, generating function, and more.

Index entries for sequences related to trees

Index entries for linear recurrences with constant coefficients, signature (140,-1715,4952,-1715,140,-1).

Formula

Faase gives a 6-term linear recurrence on his web page:

a(1) = 8,

a(2) = 1152,

a(3) = 147000,

a(4) = 18643968,

a(5) = 2363741512,

a(6) = 299675376000 and

a(n) = 140a(n-1) - 1715a(n-2) + 4952a(n-3) - 1715a(n-4) + 140a(n-5) - a(n-6).

G.f.: 8x(1+4x-70x^2+4x^3+x^4)/((x^2-4x+1)(x^4-136x^3+1170x^2-136x+1)). [R. J. Mathar, Dec 16 2008]

a(n) = 8*A001353(n)*A001110(n). [R. K. Guy, seqfan list, Mar 28 2009] [R. J. Mathar, Jun 03 2009]

Mathematica

LinearRecurrence[{140, -1715, 4952, -1715, 140, -1}, {8, 1152, 147000, 18643968, 2363741512, 299675376000}, 40] (* Harvey P. Dale, Mar 05 2013 *)

Crossrefs

Sequence in context: A246114 A229164 A357543 * A221084 A117084 A201985

Adjacent sequences: A003764 A003765 A003766 * A003768 A003769 A003770

Keyword

nonn

Author

Frans J. Faase

Extensions

Added recurrence from Faase's web page. - N. J. A. Sloane, Feb 03 2009

Title corrected by Paul Raff, Mar 06 2009

Status

approved