OFFSET
0,3
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..1000
FORMULA
a(n) ~ p / (sqrt(5) * r^(n+1)), where r = (sqrt(5)-1)/2 and p = Product_{n>1} 1/(1 - r^n - r^(2*n)) = 4.64451592505133910330213147... . - Vaclav Kotesovec, Nov 16 2016
MAPLE
F:= n-> combinat[fibonacci](n+1):
b:= proc(n, i) option remember; `if`(n=0 or i=1, F(n),
add((t-> b(t, min(t, i-1)))(n-i*j)*F(j), j=0..n/i))
end:
a:= n-> b(n$2):
seq(a(n), n=0..39); # Alois P. Heinz, Aug 24 2019
MATHEMATICA
nmax = 50; CoefficientList[Series[1/Product[1-x^k-x^(2*k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 16 2016 *)
PROG
(PARI) al(n)=Vec(1/prod(k=1, n, 1-x^k-x^(2*k)+x*O(x^n)))
(Magma) m:=50; R<x>:=PowerSeriesRing(Rationals(), m); Coefficients(R!(1/(&*[(1-x^k-x^(2*k)): k in [1..100]]))); // G. C. Greubel, Oct 24 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Franklin T. Adams-Watters, Jul 16 2009
STATUS
approved