A307738 Number of partitions of n^3 into at most n cubes.

1, 1, 1, 1, 1, 1, 3, 4, 7, 18, 36, 66, 157, 329, 728, 1611, 3655, 8062, 18154, 40358, 89807, 199778, 444419, 984422, 2183461, 4827756, 10651083, 23465459, 51576034, 113092423, 247546849, 540538832, 1177836149, 2560897979, 5555722749, 12025952101, 25976048200

Offset: 0

Author

Ilya Gutkovskiy, Apr 25 2019

Keywords

• nonn

Comments

Does a(n+1) / a(n) ~ 2? - David A. Corneth, Sep 27 2019

Examples

			7^3 =
1^3 + 1^3 + 5^3 + 6^3 =
1^3 + 1^3 + 3^3 + 4^3 + 5^3 + 5^3 =
1^3 + 2^3 + 3^3 + 3^3 + 4^3 + 6^3,
so a(7) = 4.
		

Links

• David A. Corneth, Table of n, a(n) for n = 0..100
• Index entries for sequences related to sums of cubes

Crossrefs

Cf. A000578, A025446-A025454, A030272, A105152, A259792, A298671, A298672, A307643, A307739.

Programs

PARI

a(n) = {my(res = 0); res=aIterate(n^3, 1, n); res }
aIterate(s, m, q) = { if(s == 0, return(1)); if(q == 0, return(0)); sum(i = m, sqrtnint(s, 3), aIterate(s - i^3, i, q-1) ) } \\ David A. Corneth, Sep 23 2019

Extensions

a(21)-a(36) from David A. Corneth, Sep 23 2019