A341493 - OEIS

A341493

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

1, 2, 14, 50, 722, 9922, 401998, 19681538, 2415542018, 400448833106, 152849502772958, 83804387156528018, 100644292294423977842, 180483873668860889130642, 686161117968330536875295134, 4001215836806010384390623471618

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

Number of perfect matchings in the graph C_n X C_{n+1} for n > 0.

LINKS

Table of n, a(n) for n=0..15.

S. N. Perepechko, The number of perfect matchings on C_m X C_n graphs, (in Russian), Information Processes, 2016, V. 16, No. 4, pp. 333-361.

Eric Weisstein's World of Mathematics, Perfect Matching

Eric Weisstein's World of Mathematics, Torus Grid Graph

FORMULA

a(n) ~ 2^(3/4) * exp(G*n*(n+1)/Pi), where G is Catalan's constant A006752. - Vaclav Kotesovec, Feb 14 2021

MATHEMATICA

Table[Product[4*Sin[(2*j - 1)*Pi/n]^2 + 4*Sin[(2*k - 1)*Pi/(n+1)]^2, {k, 1, n+1}, {j, 1, n}]^(1/4), {n, 0, 15}] // Round (* Vaclav Kotesovec, Feb 14 2021 *)

PROG

(PARI) default(realprecision, 120);

a(n) = round(prod(j=1, n, prod(k=1, n+1, 4*sin((2*j-1)*Pi/n)^2+4*sin((2*k-1)*Pi/(n+1))^2))^(1/4));

CROSSREFS

Cf. A162484, A220864, A230033, A231087, A231485, A232804, A253678, A281583, A281679, A308761, A309018, A335586.

Sequence in context: A153978 A214908 A143553 * A064363 A363706 A259125

Adjacent sequences: A341490 A341491 A341492 * A341494 A341495 A341496

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Feb 13 2021

STATUS

approved