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A003751
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Number of spanning trees in K_5 x P_n.
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1
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125, 300125, 663552000, 1464514260125, 3232184906328125, 7133430745792512000, 15743478429512478120125, 34745849760772636969860125, 76684074678559433693601792000, 169241718069731503830237768828125, 373516395095822778319979141039280125
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OFFSET
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1,1
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COMMENTS
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This is a divisibility sequence.
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REFERENCES
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F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154.
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LINKS
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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.
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 to divisibility sequences
Index entries for sequences related to trees
Index entries for linear recurrences with constant coefficients, signature (2255, -105985, 105985, -2255, 1).
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FORMULA
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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
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MATHEMATICA
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(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 *)
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CROSSREFS
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Sequence in context: A050640 A161354 A318258 * A120807 A013836 A048563
Adjacent sequences: A003748 A003749 A003750 * A003752 A003753 A003754
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KEYWORD
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nonn
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AUTHOR
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Frans J. Faase
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EXTENSIONS
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Added recurrence from Faase's web page. - N. J. A. Sloane, Feb 03 2009
More terms from Harvey P. Dale, Apr 24 2013
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STATUS
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approved
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