

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
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OFFSET

1,1


REFERENCES

F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129154.


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), 129154.
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(n1)  102a(n2) + 44a(n3)  a(n4), n>4.
G.f.: x*(x^343*x^2+87*x29)/(x^444*x^3+102*x^244*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(n1)102*Self(n2)+44*Self(n3)Self(n4): n in [1..20]]; // Vincenzo Librandi, Oct 14 2013
(PARI) Vec(x*(x^343*x^2+87*x29)/(x^444*x^3+102*x^244*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



