A152189 Product_{k=1..floor((n-1)/2)} (1 + 4*cos(k*Pi/n)^2)*(1 + 4*sin(k*Pi/n)^2).

1, 1, 1, 8, 9, 55, 64, 377, 441, 2584, 3025, 17711, 20736, 121393, 142129, 832040, 974169, 5702887, 6677056, 39088169, 45765225, 267914296, 313679521, 1836311903, 2149991424, 12586269025, 14736260449, 86267571272, 101003831721, 591286729879, 692290561600

Offset

0,4

Comments

It appears that limit(sqrt(a(n+2)/a(n)), n->Infinity) = 1+(sqrt(5)+1)/2.

Links

Table of n, a(n) for n=0..30.

Formula

Empirical g.f.: (x^6+x^5-9*x^4+7*x^2-x-1) / ((x-1)*(x+1)*(x^2-3*x+1)*(x^2+3*x+1)). - Colin Barker, Apr 11 2014

Mathematica

f[n_] = Product[(1 + 4*Cos[k*Pi/n]^2)*(1 + 4*Sin[k*Pi/n]^2), {k, 1, Floor[(n - 1)/2]}]; Table[N[f[n]], {n, 0, 30}]; Round[%] (* corrected by Colin Barker, Apr 11 2014 *)

Prog

(PARI) a(n) = round(prod(k=1, floor((n-1)/2), (1+4*cos(k*Pi/n)^2)*(1+4*sin(k*Pi/n)^2))) \\ Colin Barker, Apr 11 2014

Crossrefs

Cf. A152191.

Sequence in context: A341526 A042847 A121330 * A042873 A342614 A033045

Adjacent sequences: A152186 A152187 A152188 * A152190 A152191 A152192

Keyword

nonn

Author

Roger L. Bagula and Gary W. Adamson, Nov 28 2008

Extensions

Two initial terms added, and several terms corrected by Colin Barker, Apr 11 2014

Status

approved