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

%I A307738 #23 Sep 28 2019 22:09:19
%S A307738 1,1,1,1,1,1,3,4,7,18,36,66,157,329,728,1611,3655,8062,18154,40358,
%T A307738 89807,199778,444419,984422,2183461,4827756,10651083,23465459,
%U A307738 51576034,113092423,247546849,540538832,1177836149,2560897979,5555722749,12025952101,25976048200
%N A307738 Number of partitions of n^3 into at most n cubes.
%C A307738 Does a(n+1) / a(n) ~ 2? - _David A. Corneth_, Sep 27 2019
%H A307738 David A. Corneth, <a href="/A307738/b307738.txt">Table of n, a(n) for n = 0..100</a>
%H A307738 <a href="/index/Su#ssq">Index entries for sequences related to sums of cubes</a>
%e A307738 7^3 =
%e A307738 1^3 + 1^3 + 5^3 + 6^3 =
%e A307738 1^3 + 1^3 + 3^3 + 4^3 + 5^3 + 5^3 =
%e A307738 1^3 + 2^3 + 3^3 + 3^3 + 4^3 + 6^3,
%e A307738 so a(7) = 4.
%o A307738 (PARI) a(n) = {my(res = 0); res=aIterate(n^3, 1, n); res }
%o A307738 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
%Y A307738 Cf. A000578, A025446-A025454, A030272, A105152, A259792, A298671, A298672, A307643, A307739.
%K A307738 nonn
%O A307738 0,7
%A A307738 _Ilya Gutkovskiy_, Apr 25 2019
%E A307738 a(21)-a(36) from _David A. Corneth_, Sep 23 2019