A341535 a(n) = sqrt(Product_{1<=j,k<=n} (4*sin((2*j-1)*Pi/(2*n))^2 + 4*sin((2*k-1)*Pi/n)^2)).

1, 2, 36, 224, 38416, 2540032, 4115479104, 3044533460992, 48656376372265216, 387018647188487143424, 62441634466575620320306176, 5221063878050546380074377019392, 8590392749565593082105293619707908096, 7476351474500749779460880888573410601336832

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..62

Formula

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

If n is odd, a(n) = 2*A341478(n). - Seiichi Manyama, Feb 19 2021

Mathematica

Table[Sqrt[Product[4*Sin[(2*j - 1)*Pi/(2*n)]^2 + 4*Sin[(2*k - 1)*Pi/n]^2, {k, 1, n}, {j, 1, n}]], {n, 0, 20}] // Round (* Vaclav Kotesovec, Feb 14 2021 *)

Prog

(PARI) default(realprecision, 120);
a(n) = round(sqrt(prod(j=1, n, prod(k=1, n, 4*sin((2*j-1)*Pi/(2*n))^2+4*sin((2*k-1)*Pi/n)^2))));

Crossrefs

Main diagonal of A341533.

Cf. A341478, A341479, A341782.

Sequence in context: A226419 A025531 A099903 * A074426 A082636 A242533

Adjacent sequences: A341532 A341533 A341534 * A341536 A341537 A341538

Keyword

nonn

Author

Seiichi Manyama, Feb 13 2021

Status

approved