A092136 Number of spanning trees in S_5 x P_n.

1, 189, 24576, 3046869, 375175625, 46151368704, 5676383392121, 698151521972709, 85867005969063936, 10560944392853518125, 1298910307853115410641, 159755407182415993503744, 19648616177810537712940081, 2416620034547514872344613709

Offset: 1

Author

Ralf Stephan, Mar 28 2004

Keywords

• nonn

Links

• P. Raff, Table of n, a(n) for n = 1..200
• F. Faase, Counting Hamiltonian cycles in product graphs
• P. Raff, Spanning Trees in Grid Graphs, arXiv:0809.2551 [math.CO], 2008.
• P. Raff, Analysis of the Number of Spanning Trees of S_5 x P_n. 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 (144, -2640, 6930, -2640, 144, -1).

Crossrefs

Cf. A001906, A004187, A049684.

Programs

Mathematica

LinearRecurrence[{7, -1}, {0, 1}, 13] LinearRecurrence[{3, -1}, {0, 1}, 13]^3 // Rest (* Jean-François Alcover, Oct 30 2018, after R. J. Mathar *)
LinearRecurrence[{144, -2640, 6930, -2640, 144, -1},{1, 189, 24576, 3046869, 375175625, 46151368704}, 14] (* Ray Chandler, Feb 28 2024 *)

Formula

a(n) = 144*a(n-1) - 2640*a(n-2) + 6930*a(n-3) - 2640*a(n-4) + 144*a(n-5) - a(n-6). [Modified by Paul Raff, Oct 30 2009]

G.f.: -x*(x^4 + 45*x^3 - 45*x-1)/(x^6 - 144*x^5 + 2640*x^4 - 6930*x^3 + 2640*x^2 - 144*x + 1). - Paul Raff (paul(AT)myraff.com), Mar 07 2009

a(n) = A004187(n)*(A001906(n))^3 = A004187(n)*A001906(n)*A049684(n). [See R. Guy, seqfan list, Mar 28 2009] - R. J. Mathar, Jun 03 2009