A302019 Expansion of 1/(1 - x*Sum_{k>=0} x^(k^3)).

1, 1, 2, 3, 5, 8, 13, 21, 34, 56, 91, 149, 243, 397, 648, 1058, 1727, 2819, 4602, 7512, 12263, 20018, 32678, 53344, 87080, 142151, 232050, 378803, 618366, 1009433, 1647819, 2689933, 4391101, 7168122, 11701387, 19101580, 31181804, 50901806, 83093134, 135642908, 221426218, 361460624

Offset: 0

Author

Ilya Gutkovskiy, Mar 30 2018

Keywords

• nonn

Links

• N. J. A. Sloane, Transforms
• Index entries for sequences related to sums of cubes

Crossrefs

Antidiagonal sums of A290054.

Cf. A010057, A302018.

Programs

Mathematica

nmax = 41; CoefficientList[Series[1/(1 - x Sum[x^k^3, {k, 0, nmax}]), {x, 0, nmax}], x]

Formula

G.f.: 1/(1 - x*Sum_{k>=0} x^(k^3)).

a(0) = 1; a(n) = Sum_{k=1..n} A010057(k-1)*a(n-k).