A357366 Expansion of Product_{k>=0} 1 / (1 - x^(2^k) - x^(2^(k+1)))^(2^k).

1, 1, 4, 5, 18, 23, 59, 82, 203, 285, 610, 895, 1838, 2733, 5217, 7950, 14763, 22713, 40526, 63239, 110652, 173891, 297529, 471420, 796706, 1268126, 2116508, 3384634, 5606444, 8991078, 14791302, 23782380, 38955441, 62737821, 102388280, 165126101, 268844542, 433970643

Offset

0,3

Links

Table of n, a(n) for n=0..37.

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

Cf. A073709, A084782, A173285, A237651.

Sequence in context: A051949 A275961 A243297 * A026902 A026755 A368029

Adjacent sequences: A357363 A357364 A357365 * A357367 A357368 A357369

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 25 2022

Status

approved