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A003747
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Number of perfect matchings (or domino tilings) in K_5 X P_2n.
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1
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56, 4181, 313501, 23508376, 1762814681, 132187592681, 9912306636376, 743290810135501, 55736898453526181, 4179524093204328056, 313408570091871078001, 23501463232797126522001, 1762296333889692618072056, 132148723578494149228882181, 9909391972053171499548091501
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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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FORMULA
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a(n) = 76*a(n-1) - 76*a(n-2) + a(n-3), n > 3.
G.f.: -x*(x^2-75*x+56)/((x-1)*(x^2-75*x+1)). - Colin Barker, Aug 30 2012
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MATHEMATICA
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CoefficientList[Series[-(x^2 - 75 x + 56)/((x - 1) (x^2 - 75 x + 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 14 2013 *)
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PROG
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(Magma) I:=[56, 4181, 313501]; [n le 3 select I[n] else 76*Self(n-1)-76*Self(n-2)+Self(n-3): n in [1..20]]; // 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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STATUS
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approved
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