A173677 Number of ways of writing n as a sum of two nonnegative cubes.

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

Offset: 0

Author

N. J. A. Sloane, Nov 24 2010

Keywords

• nonn
• easy

Comments

Order matters. This is the coefficient of q^n in the expansion of {Sum_{m>=0} q^(m^3)}^2.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A004829, A008451, A010057, A051343, A173676.

Sums of k cubes, number of ways of writing n as, for k=1..9: A010057, A173677, A051343, A173678, A173679, A173680, A173676, A173681, A173682.

Programs

PARI

list(n)=my(q='q);Vec(sum(m=0,(n+.5)^(1/3),q^(m^3),O(q^(n+1)))^2) \\ Charles R Greathouse IV, Jun 07 2012

Formula

a(n) = Sum_{k=0..n} c(k) * c(n-k), where c = A010057. - Wesley Ivan Hurt, Nov 09 2023