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A307738
Number of partitions of n^3 into at most n cubes.
3
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
0,7
COMMENTS
Does a(n+1) / a(n) ~ 2? - David A. Corneth, Sep 27 2019
EXAMPLE
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.
PROG
(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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 25 2019
EXTENSIONS
a(21)-a(36) from David A. Corneth, Sep 23 2019
STATUS
approved