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 A003751 Number of spanning trees in K_5 x P_n. 1
 125, 300125, 663552000, 1464514260125, 3232184906328125, 7133430745792512000, 15743478429512478120125, 34745849760772636969860125, 76684074678559433693601792000, 169241718069731503830237768828125, 373516395095822778319979141039280125 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This is a divisibility sequence. 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, Results from the counting program P. Raff, Spanning Trees in Grid Graphs. 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. Index entries for linear recurrences with constant coefficients, signature (2255, -105985, 105985, -2255, 1). FORMULA a(n) = 2255a(n-1)- 105985a(n-2) +105985a(n-3) -2255a(n-4) +a(n-5). a(n)=125*(A004187(n))^4 = 125*(A049682(n))^2. [R. Guy, seqfan list, Mar 28 2009] [From R. J. Mathar, Jun 03 2009] G.f.: -(125x(x^3+146x^2+146x+1)/(x^5-2255x^4+105985x^3-105985x^2+2255x-1)) [Paul Raff, Oct 29, 2009] a(n) = 125*F(4n)^4/81. - R. K. Guy, Feb 24 2010 MATHEMATICA (125*Fibonacci[4*Range]^4)/81 (* or *) LinearRecurrence[ {2255, -105985, 105985, -2255, 1}, {125, 300125, 663552000, 1464514260125, 3232184906328125}, 20] (* Harvey P. Dale, Apr 24 2013 *) CROSSREFS Sequence in context: A050640 A161354 A318258 * A120807 A013836 A048563 Adjacent sequences:  A003748 A003749 A003750 * A003752 A003753 A003754 KEYWORD nonn AUTHOR EXTENSIONS Added recurrence from Faase's web page. - N. J. A. Sloane, Feb 03 2009 More terms from Harvey P. Dale, Apr 24 2013 STATUS approved

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Last modified November 12 17:06 EST 2019. Contains 329058 sequences. (Running on oeis4.)