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A152192
a(n) = Product_{k=1..floor((n-1)/2)} (1 + 4*cos(2*Pi*k/n)^2).
0
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
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
Sequence in context: A209143 A243274 A119914 * A290889 A120924 A079285
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms and edited by Colin Barker, Michel Marcus, and Joerg Arndt, Apr 11 2014
STATUS
approved