OFFSET
0,3
FORMULA
G.f. A(x) satisfies: A(x) = A(x^2)^2 / (1 - x - x^2).
a(n) ~ c * phi^(n+1) / sqrt(5), where c = Product_{k>=1} 1/(1 - x^(2^k) - x^(2^(k+1)))^(2^k) = 11.1991985012843182084779984477952870732899201240395056... and phi = A001622 is the golden ratio. - Vaclav Kotesovec, Oct 08 2022
MATHEMATICA
nmax = 37; CoefficientList[Series[Product[1/(1 - x^(2^k) - x^(2^(k + 1)))^(2^k), {k, 0, Floor[Log[2, nmax]] + 1}], {x, 0, nmax}], x]
nmax = 37; A[_] = 1; Do[A[x_] = A[x^2]^2/(1 - x - x^2) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Sep 25 2022
STATUS
approved