A003745 Number of spanning trees in (K_5 - e) X P_n.

75, 128625, 199065600, 307147367625, 473862674071875, 731065883885568000, 1127873690900648512275, 1740060755637940344737625, 2684530596730102104276172800

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

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 linear recurrences with constant coefficients, signature (1645, -160129, 3747310, -7579606, 3747310, -160129, 1645, -1).

Formula

a(n) = 1645*a(n-1) - 160129*a(n-2) + 3747310*a(n-3) - 7579606*a(n-4) + 3747310*a(n-5) - 160129*a(n-6) + 1645*a(n-7) - a(n-8). - Modified by Paul Raff, Oct 29 2009

G.f.: -75x(x^6 + 70x^5 - 6838x^4 + 6838x^2 - 70x - 1)/(x^8 - 1645x^7 + 160129x^6 - 3747310x^5 + 7579606x^4 - 3747310x^3 + 160129x^2 - 1645x + 1). - Paul Raff, Oct 29 2009

a(n) = 75*A001906(n)*(A004187(n))^3 [R. K. Guy, via seqfan list, Mar 28 2009]. - R. J. Mathar, Jun 03 2009

Mathematica

75 LinearRecurrence[{1645, -160129, 3747310, -7579606, 3747310, -160129, 1645, -1}, {1, 1715, 2654208, 4095298235, 6318168987625, 9747545118474240, 15038315878675313497, 23200810075172537929835}, 20] (* Jean-François Alcover, Oct 07 2018 *)

Crossrefs

Sequence in context: A263064 A085404 A110100 * A301468 A068942 A116234

Adjacent sequences: A003742 A003743 A003744 * A003746 A003747 A003748

Keyword

nonn

Author

Frans J. Faase

Extensions

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

Status

approved