A341543 a(n) = sqrt( Product_{j=1..n} Product_{k=1..2} (4*sin((2*j-1)*Pi/(2*n))^2 + 4*sin((2*k-1)*Pi/2)^2) ).

8, 36, 200, 1156, 6728, 39204, 228488, 1331716, 7761800, 45239076, 263672648, 1536796804, 8957108168, 52205852196, 304278005000, 1773462177796, 10336495061768, 60245508192804, 351136554095048, 2046573816377476, 11928306344169800

Offset: 1

Author

Seiichi Manyama, Feb 14 2021

Keywords

• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (7, -7, 1)

Crossrefs

Column k=2 of A341533.

Cf. A001541.

Programs

PARI

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

Formula

a(n) = 7*a(n-1) - 7*a(n-2) + a(n-3).

a(n) = 6*a(n-1) - a(n-2) - 8.

a(n) = 2*(A001541(n) + 1). - Hugo Pfoertner, Feb 14 2021

G.f.: 4*x*(2 - 5*x + x^2)/((1 - x)*(1 - 6*x + x^2)). - Vaclav Kotesovec, Feb 14 2021