A173681 Number of ways of writing n as a sum of 8 nonnegative cubes.

1, 8, 28, 56, 70, 56, 28, 8, 9, 56, 168, 280, 280, 168, 56, 8, 28, 168, 420, 560, 420, 168, 28, 0, 56, 280, 560, 568, 336, 224, 280, 280, 238, 336, 428, 336, 406, 840, 1120, 840, 392, 224, 168, 224, 840, 1680, 1680, 840, 196, 56, 28, 280, 1120, 1680, 1148, 448, 428, 568, 420, 448, 868, 840, 448, 840, 1689, 1736, 1008, 616, 616, 336, 476, 1688, 2576

Offset: 0

Author

N. J. A. Sloane, Nov 25 2010

Keywords

• nonn

Comments

Order matters. This is the coefficient of q^n in the expansion of {Sum_{m>=0} q^(m^3)}^8.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• L. E. Dickson, All integers except 23 and 239 are sums of eight cubes, Bull. Amer. Math. Soc. 45 (1939), 588-591.

Crossrefs

Cf. A004830, A173677.

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

lista(n)=my(q='q); Vec(sum(m=0, (n+.5)^(1/3), q^(m^3), O(q^(n+1)))^8); \\ Michel Marcus, Apr 12 2016