A173676 Number of ways of writing n as a sum of seven nonnegative cubes.

1, 7, 21, 35, 35, 21, 7, 1, 7, 42, 105, 140, 105, 42, 7, 0, 21, 105, 210, 210, 105, 21, 0, 0, 35, 140, 210, 147, 77, 105, 140, 105, 77, 112, 105, 77, 210, 420, 420, 210, 63, 42, 21, 105, 420, 630, 420, 105, 7, 7, 0, 140, 420, 420, 161, 105, 211, 210, 105, 126, 210, 105, 105, 420, 637, 462, 210, 182, 147, 42, 217, 630, 672, 420, 420, 427, 210, 42

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)}^7.

It is known that a(n)>0 if n is even and > 454.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• N. D. Elkies, Every even number greater than 454 is the sum of seven cubes, arXiv:1009.3983

Crossrefs

Cf. A004829, A008451.

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