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A298934 Number of partitions of n^2 into distinct cubes.

%I A298934 #8 Jan 29 2018 16:26:03
%S A298934 1,1,0,1,0,0,1,0,1,0,1,0,0,0,0,2,0,1,0,0,0,1,0,0,1,0,0,3,1,0,0,0,0,0,
%T A298934 0,3,3,1,0,3,0,2,4,0,0,1,0,0,2,3,1,1,0,6,3,6,1,6,0,3,9,0,6,6,7,0,10,3,
%U A298934 3,6,0,8,6,13,2,10,9,10,19,2,14,21,7,2,25
%N A298934 Number of partitions of n^2 into distinct cubes.
%H A298934 Alois P. Heinz, <a href="/A298934/b298934.txt">Table of n, a(n) for n = 0..1000</a>
%H A298934 <a href="/index/Su#ssq">Index entries for sequences related to sums of cubes</a>
%H A298934 <a href="/index/Par#part">Index entries for related partition-counting sequences</a>
%F A298934 a(n) = [x^(n^2)] Product_{k>=1} (1 + x^(k^3)).
%F A298934 a(n) = A279329(A000290(n)).
%e A298934 a(15) = 2 because we have [216, 8, 1] and [125, 64, 27, 8, 1].
%p A298934 b:= proc(n, i) option remember; `if`(n=0, 1,
%p A298934       `if`(n>i^2*(i+1)^2/4, 0, b(n, i-1)+
%p A298934       `if`(i^3>n, 0, b(n-i^3, i-1))))
%p A298934     end:
%p A298934 a:= n-> b(n^2, n):
%p A298934 seq(a(n), n=0..100);  # _Alois P. Heinz_, Jan 29 2018
%t A298934 Table[SeriesCoefficient[Product[1 + x^k^3, {k, 1, Floor[n^(2/3) + 1]}], {x, 0, n^2}], {n, 0, 84}]
%Y A298934 Cf. A000290, A000578, A030272, A030273, A218495, A259792, A279329, A298672, A298848, A298935.
%K A298934 nonn
%O A298934 0,16
%A A298934 _Ilya Gutkovskiy_, Jan 29 2018