A003773 Number of spanning trees in K_4 X P_n.
16, 3456, 686000, 135834624, 26894628304, 5325000912000, 1054323287943536, 208750686023540736, 41331581509440922000, 8183444388183674181504, 1620280657278860350213424, 320807386696826179092096000
Offset: 1
Keywords
References
- F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154.
Links
- Paul Raff, Jun 04 2008, Table of n, a(n) for n = 1..15
- 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_3 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 (204,-1190,204,-1).
Programs
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Mathematica
LinearRecurrence[{204, -1190, 204, -1},{16, 3456, 686000, 135834624},12] (* Ray Chandler, Aug 11 2015 *)
Formula
a(1) = 16,
a(2) = 3456,
a(3) = 686000,
a(4) = 135834624,
a(5) = 26894628304 and
a(n) = 205a(n-1) - 1394a(n-2) + 1394a(n-3) - 205a(n-4) + a(n-5).
a(n) = 204*a(n-1) - 1190*a(n-2) + 204*a(n-3) - a(n-4). - Paul Raff, Jun 04 2008
G.f.: 16x(1+12x+x^2)/((1-6x+x^2)(x^2-198x+1)). a(n) = 35*A097731(n-1)/2 - 3*A001109(n)/2. - R. J. Mathar, Dec 16 2008
a(n)=16*(A001109(n))^3=16*A001109(n)*A001110(n). [R. Guy, seqfan list, Mar 28 2009] - R. J. Mathar, Jun 03 2009
Extensions
More terms from Paul Raff, Jun 04 2008
Added recurrence from Faase's web page. - N. J. A. Sloane, Feb 03 2009