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A003731
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Number of Hamiltonian cycles in C_5 X P_n.
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5
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1, 5, 30, 160, 850, 4520, 24040, 127860, 680040, 3616880, 19236840, 102313600, 544168000, 2894227280, 15393318880, 81871340160, 435443220000, 2315960597120, 12317733383040, 65513444349760, 348441653760640, 1853231611930880, 9856649945242240, 52423856531251200
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OFFSET
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1,2
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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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FORMULA
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a(n) = 6a(n-1) - 4a(n-2) + 2a(n-3), n>3.
G.f.: x*(1-x+4*x^2-2*x^3)/(1-6*x+4*x^2-2*x^3). - Colin Barker, Sep 01 2012
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MATHEMATICA
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CoefficientList[Series[(1 - x + 4 x^2 - 2 x^3)/(1 - 6 x + 4 x^2 - 2 x^3), {x, 0, 40}], x] (* Vincenzo Librandi, Oct 14 2013 *)
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PROG
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(Magma) I:=[1, 5, 30, 160]; [n le 4 select I[n] else 6*Self(n-1)-4*Self(n-2)+2*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Oct 14 2013 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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