OFFSET
0,4
COMMENTS
It appears that limit(sqrt(a(n+2)/a(n)), n->Infinity) = 1+(sqrt(5)+1)/2.
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
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