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A003735 Number of perfect matchings (or domino tilings) in W_5 X P_2n. 1
29, 1189, 49401, 2053641, 85373589, 3549138989, 147544320241, 6133692298001, 254989017189389, 10600368542888629, 440677071050573801, 18319766917914642201, 761586844367955639429, 31660584117320436988989, 1316189472103884945976801, 54716448693989525183595041 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..600

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 sequences related to dominoes

Index entries for linear recurrences with constant coefficients, signature (44,-102,44,-1).

FORMULA

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

MATHEMATICA

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 *)

PROG

(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

(PARI) Vec(-x*(x^3-43*x^2+87*x-29)/(x^4-44*x^3+102*x^2-44*x+1)+O(x^99)) \\ Charles R Greathouse IV, Jun 23 2020

CROSSREFS

Sequence in context: A210303 A268461 A025761 * A159479 A264351 A195740

Adjacent sequences:  A003732 A003733 A003734 * A003736 A003737 A003738

KEYWORD

nonn,easy

AUTHOR

Frans J. Faase

STATUS

approved

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Last modified November 30 06:47 EST 2020. Contains 338781 sequences. (Running on oeis4.)