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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
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.
P. Raff, Spanning Trees in Grid Graphs, arXiv:0809.2551 [math.CO], 2008.
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[20]]^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
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 June 17 22:48 EDT 2024. Contains 373466 sequences. (Running on oeis4.)