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%I #18 Dec 04 2020 15:56:07
%S 0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,
%T 0,1,0,1,0,0,0,0,1,0,1,0,0,0,0,1,0,1,0,0,0,0,1,0,1,0,0,1,0,1,0,1,0,0,
%U 1,0,1,0,2,0,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,1,0,1,0,1
%N Number of partitions of n into 9 positive cubes.
%H Alois P. Heinz, <a href="/A025462/b025462.txt">Table of n, a(n) for n = 0..65536</a>
%H <a href="/index/Su#ssq">Index entries for sequences related to sums of cubes</a>
%F a(n) = [x^n y^9] Product_{k>=1} 1/(1 - y*x^(k^3)). - _Ilya Gutkovskiy_, Apr 23 2019
%p b:= proc(n, i, t) option remember; `if`(n=0, `if`(t=0, 1, 0),
%p `if`(i<1 or t<1, 0, b(n, i-1, t)+
%p `if`(i^3>n, 0, b(n-i^3, i, t-1))))
%p end:
%p a:= n-> b(n, iroot(n, 3), 9):
%p seq(a(n), n=0..120); # _Alois P. Heinz_, Dec 21 2018
%t b[n_, i_, t_] := b[n, i, t] = If[n == 0, If[t == 0, 1, 0], If[i < 1 || t < 1, 0, b[n, i - 1, t] + If[i^3 > n, 0, b[n - i^3, i, t - 1]]]];
%t a[n_] := b[n, n^(1/3) // Floor, 9];
%t a /@ Range[0, 120] (* _Jean-François Alcover_, Dec 04 2020, after _Alois P. Heinz_ *)
%Y Cf. A000578 (cubes).
%Y Column k=9 of A320841.
%K nonn
%O 0,73
%A _David W. Wilson_
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