A309026 Expansion of x * Product_{k>=0} (1 + x^(2^k) + x^(2^(k+4))).

0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 3, 2, 2, 1, 3, 2, 2, 1, 3, 2, 2, 1, 3, 2, 2, 1, 4, 2, 2, 1, 4, 2, 2, 1, 4, 2, 2, 1, 4, 2, 2, 1, 5, 3, 3, 2, 4, 2, 2, 1, 5, 3, 3, 2, 4, 2, 2, 1, 6, 3, 4, 2, 4, 2, 2, 1, 6, 3, 4, 2, 4, 2, 2, 1, 7, 4, 4, 2

Offset: 0

Author

Ilya Gutkovskiy, Jul 07 2019

Keywords

• nonn

Crossrefs

Cf. A002487, A112970, A309025.

Programs

Mathematica

nmax = 100; CoefficientList[Series[x Product[(1 + x^(2^k) + x^(2^(k + 4))), {k, 0, Floor[Log[2, nmax]] + 1}], {x, 0, nmax}], x]

Formula

a(n) = 0 for n <= 0, a(1) = 1; a(2*n) = a(n), a(2*n+1) = a(n-7) + a(n+1).