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A003737
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Number of Hamiltonian cycles in W_5 X P_n.
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1
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4, 92, 1432, 22632, 357952, 5660752, 89521984, 1415743552, 22389250144, 354074376800, 5599502597088, 88553228914208, 1400423379497056, 22146969296658080, 350242830993566816, 5538908688560111008, 87594967677616439904, 1385268975148564102048, 21907310252932371420768
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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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Vincenzo Librandi, Table of n, a(n) for n = 1..850
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
Index entries for linear recurrences with constant coefficients, signature (13,50,-80,-120,188,32,-16).
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FORMULA
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a(1) = 4,
a(2) = 92,
a(3) = 1432,
a(4) = 22632,
a(5) = 357952,
a(6) = 5660752,
a(7) = 89521984,
a(8) = 1415743552, and
a(n) = 13a(n-1) + 50a(n-2) - 80a(n-3) - 120a(n-4) + 188a(n-5) + 32a(n-6) - 16a(n-7).
G.f.: 4*x*(2*x^2 -3*x -1)*(8*x^5 -40*x^4 +22*x^3 +10*x^2 -7*x -1)/(16*x^7 -32*x^6 -188*x^5 +120*x^4 +80*x^3 -50*x^2 -13*x +1). - Colin Barker, Aug 31 2012
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MATHEMATICA
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CoefficientList[Series[4 (2 x^2 - 3 x - 1) (8 x^5 - 40 x^4 + 22 x^3 + 10 x^2 - 7 x - 1)/(16 x^7 - 32 x^6 - 188 x^5 + 120 x^4 + 80 x^3 - 50 x^2 - 13 x + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 14 2013 *)
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PROG
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(MAGMA) I:=[4, 92, 1432, 22632, 357952, 5660752, 89521984, 1415743552]; [n le 8 select I[n] else 13*Self(n-1)+50*Self(n-2)-80*Self(n-3)-120*Self(n-4)+188*Self(n-5)+32*Self(n-6)-16*Self(n-7): n in [1..20]]; // Vincenzo Librandi, Oct 14 2013
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CROSSREFS
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Sequence in context: A209984 A065574 A113252 * A265238 A322769 A012071
Adjacent sequences: A003734 A003735 A003736 * A003738 A003739 A003740
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KEYWORD
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nonn,easy
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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
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STATUS
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approved
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