A369572 Expansion of Product_{k>=1} (1 + x^(k^2)) * (1 + x^(k^3)).

1, 2, 1, 0, 1, 2, 1, 0, 1, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 4, 5, 3, 3, 5, 5, 3, 2, 3, 5, 5, 5, 7, 7, 5, 5, 6, 5, 4, 5, 7, 7, 5, 5, 8, 9, 6, 6, 10, 10, 6, 6, 9, 9, 6, 5, 10, 13, 9, 9, 15, 14, 7, 6, 11, 13, 9, 8, 15, 19, 13, 10, 16, 18, 12, 10, 16

Offset: 0

Author

Vaclav Kotesovec, Jan 26 2024

Keywords

• nonn

Comments

Convolution of A033461 and A279329.

a(n) is the number of pairs (Q(k), P(n-k)), 0<=k<=n, where Q(k) is a partition of k into distinct squares and P(n-k) is a partition of n-k into distinct cubes.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A033461, A279329.

Programs

Mathematica

nmax = 200; CoefficientList[Series[Product[(1+x^(k^2))*(1+x^(k^3)), {k, 1, nmax^(1/2)}], {x, 0, nmax}], x]