OFFSET
0,4
LINKS
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
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula and Gary W. Adamson, Nov 28 2008
EXTENSIONS
STATUS
approved