A280618 Expansion of (Sum_{k>=1} x^(k^3))^2.

0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 0

Author

Ilya Gutkovskiy, Jan 06 2017

Keywords

• nonn

Comments

Number of ways to write n as an ordered sum of two positive cubes.

Examples

			a(9) = 2 because we have [8, 1] and [1, 8].
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..65537
• Eric Weisstein's World of Mathematics, Cubic Number
• Index entries for sequences related to sums of cubes

Crossrefs

Cf. A000578, A001235 (positions of terms > 3), A003325 (of nonzero terms), A010057, A063725, A173677.

Programs

Mathematica

nmax = 150; CoefficientList[Series[(Sum[x^(k^3), {k, 1, nmax}])^2, {x, 0, nmax}], x]

PARI

A010057(n) = ispower(n, 3);
A280618(n) = if(n<2, 0, sum(r=1,sqrtnint(n-1,3),A010057(n-(r^3)))); \\ Antti Karttunen, Nov 30 2021

Formula

G.f.: (Sum_{k>=1} x^(k^3))^2.