A231087 Number of perfect matchings in graph C_3 x C_{2n}.

50, 224, 1058, 5054, 24200, 115934, 555458, 2661344, 12751250, 61094894, 292723208, 1402521134, 6719882450, 32196891104, 154264573058, 739125974174, 3541365297800, 16967700514814, 81297137276258, 389517985866464, 1866292792056050, 8941945974413774, 42843437080012808, 205275239425650254

Offset

2,1

Links

Paolo Xausa, Table of n, a(n) for n = 2..1000

Index entries for sequences related to dominoes.

Index entries for linear recurrences with constant coefficients, signature (6,-6,1).

Formula

a(n) = 2*(((sqrt(7)+sqrt(3))/2)^n + ((sqrt(7)-sqrt(3))/2)^n)^2.

G.f.: 2*x^2*(25-38*x+7*x^2)/((1-x)*(1-5*x+x^2)).

From Seiichi Manyama, Feb 14 2021: (Start)

a(n) = sqrt( Product_{j=1..n} Product_{k=1..3} (4*sin((2*j-1)*Pi/(2*n))^2 + 4*sin((2*k-1)*Pi/3)^2) ).

a(n) = 5*a(n-1) - a(n-2) - 12. (End)

a(n) = 6*A054493(n-1) + 8. - Peter Bala, May 17 2025

E.g.f.: 4*exp(x)*(1 + exp(3*x/2)*cosh(sqrt(21)*x/2)) - 8 - 14*x. - Stefano Spezia, Apr 04 2026

Mathematica

LinearRecurrence[{6, -6, 1}, {50, 224, 1058}, 25] (* Paolo Xausa, May 08 2026 *)

Prog

(PARI) Vec(2*x^2*(25-38*x+7*x^2)/((1-x)*(1-5*x+x^2))+O(x^66)) \\ Joerg Arndt, Nov 03 2013
(PARI) default(realprecision, 120);
a(n) = round(sqrt(prod(j=1, n, prod(k=1, 3, 4*sin((2*j-1)*Pi/(2*n))^2+4*sin((2*k-1)*Pi/3)^2)))); \\ Seiichi Manyama, Feb 14 2021

Crossrefs

Cf. A054493, A220864.

Sequence in context: A186843 A250527 A251065 * A235956 A197971 A235567

Adjacent sequences: A231084 A231085 A231086 * A231088 A231089 A231090

Keyword

easy,nonn

Author

Sergey Perepechko, Nov 03 2013

Status

approved