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A003741
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Number of perfect matchings (or domino tilings) in O_5 X P_2n.
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0
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40, 2197, 121735, 6748096, 374079619, 20737143595, 1149566489968, 63726386332735, 3532681575875629, 195834721732832344, 10856126548559080585, 601810968956118729913
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OFFSET
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1,1
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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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Table of n, a(n) for n=1..12.
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 Hamilton cycles in product graphs
F. Faase, Results from the counting program
F. Faase, Counting Hamilton cycles in product graphs
Index entries for sequences related to dominoes
Index to sequences with linear recurrences with constant coefficients, signature (65,-548,995,-548,65,-1).
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FORMULA
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If b(n) denotes the number of perfect matchings (or domino tilings) in O_5 X P_n we have:
b(1) = 0,
b(2) = 40,
b(3) = 0,
b(4) = 2197,
b(5) = 0,
b(6) = 121735,
b(7) = 0,
b(8) = 6748096,
b(9) = 0,
b(10) = 374079619,
b(11) = 0,
b(12) = 20737143595, and
b(n) = 65b(n-2) - 548b(n-4) + 995b(n-6) - 548b(n-8) + 65b(n-10) - b(n-12).
G.f.: -x*(x^5 -64*x^4 +523*x^3 -850*x^2 +403*x -40)/(x^6 -65*x^5 +548*x^4 -995*x^3 +548*x^2 -65*x +1). [Colin Barker, Aug 31 2012]
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CROSSREFS
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Sequence in context: A060056 A223177 A140729 * A049215 A221658 A188154
Adjacent sequences: A003738 A003739 A003740 * A003742 A003743 A003744
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KEYWORD
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nonn,easy
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AUTHOR
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Frans Faase (Frans_LiXia(AT)wxs.nl)
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EXTENSIONS
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Added recurrence from Faase's web page. - N. J. A. Sloane, Feb 03 2009
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STATUS
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approved
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