A152192 a(n) = Product_{k=1..floor((n-1)/2)} (1 + 4*cos(2*Pi*k/n)^2).

1, 1, 1, 2, 1, 5, 4, 13, 9, 34, 25, 89, 64, 233, 169, 610, 441, 1597, 1156, 4181, 3025, 10946, 7921, 28657, 20736, 75025, 54289, 196418, 142129, 514229, 372100, 1346269, 974169, 3524578, 2550409, 9227465, 6677056, 24157817, 17480761, 63245986, 45765225

Offset

0,4

Links

Table of n, a(n) for n=0..40.

Index entries for linear recurrences with constant coefficients, signature (0,2,0,2,0,-1).

Formula

Lim_{n->infinity} sqrt(a(n+2)/a(n)) = (sqrt(5) + 1)/2.

G.f.: (1+x^6-x^5-3*x^4-x^2+x)/((x^2+1)*(x^2+x-1)*(x^2-x-1)). - Maksym Voznyy (voznyy(AT)mail.ru), Jul 26 2009

For n > 0, a(n) = Fibonacci(n) for n odd, and Fibonacci(n/2)^2 for n even. - Greg Dresden, Oct 16 2021

Mathematica

a[n_] := Product[(1 + 4*Cos[2*Pi*k/n]^2), {k, 1, Floor[(n - 1)/2]}]; a = Table[N[a[n]], {n, 0, 30}]
Join[{1}, Table[If[EvenQ[n], Fibonacci[(n)/2]^2, Fibonacci[n]], {n, 1, 30}]] (* Greg Dresden, Oct 16 2021 *)

Prog

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

Crossrefs

Cf. A152189, A152191.

Sequence in context: A209143 A243274 A119914 * A290889 A120924 A079285

Adjacent sequences: A152189 A152190 A152191 * A152193 A152194 A152195

Keyword

nonn,easy

Author

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

Extensions

More terms and edited by Colin Barker, Michel Marcus, and Joerg Arndt, Apr 11 2014

Status

approved