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A003735
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Number of perfect matchings (or domino tilings) in W_5 X P_2n.
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1
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29, 1189, 49401, 2053641, 85373589, 3549138989, 147544320241, 6133692298001, 254989017189389, 10600368542888629, 440677071050573801, 18319766917914642201, 761586844367955639429, 31660584117320436988989, 1316189472103884945976801, 54716448693989525183595041
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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) = 44a(n-1) - 102a(n-2) + 44a(n-3) - a(n-4), n>4.
G.f.: -x*(x^3-43*x^2+87*x-29)/(x^4-44*x^3+102*x^2-44*x+1). - Colin Barker, Aug 30 2012
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MATHEMATICA
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CoefficientList[Series[-(x^3 - 43 x^2 + 87 x - 29)/(x^4 - 44 x^3 + 102 x^2 - 44 x + 1), {x, 0, 40}], x] (* Vincenzo Librandi, Oct 14 2013 *)
LinearRecurrence[{44, -102, 44, -1}, {29, 1189, 49401, 2053641}, 20] (* Harvey P. Dale, Jul 19 2018 *)
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PROG
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(Magma) I:=[29, 1189, 49401, 2053641]; [n le 4 select I[n] else 44*Self(n-1)-102*Self(n-2)+44*Self(n-3)-Self(n-4): 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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