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A303484 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals: A(n,k) = [x^(n^3)] (1/(1 - x))*(Sum_{j>=0} x^(j^3))^k.

%I A303484 #4 Apr 24 2018 19:11:49
%S A303484 1,1,1,1,2,1,1,3,3,1,1,4,6,4,1,1,5,11,11,5,1,1,6,20,30,18,6,1,1,7,37,
%T A303484 84,66,26,7,1,1,8,70,237,241,115,37,8,1,1,9,135,662,853,500,200,50,9,
%U A303484 1,1,10,264,1780,2847,2093,1012,302,63,10,1,1,11,520,4536,9033,8451,4914,1769,441,80,11,1
%N A303484 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals: A(n,k) = [x^(n^3)] (1/(1 - x))*(Sum_{j>=0} x^(j^3))^k.
%C A303484 A(n,k) is the number of nonnegative solutions to (x_1)^3 + (x_2)^3 + ... + (x_k)^3 <= n^3.
%H A303484 <a href="/index/Su#ssq">Index entries for sequences related to sums of cubes</a>
%e A303484 Square array begins:
%e A303484 1,  1,   1,    1,    1,     1,  ...
%e A303484 1,  2,   3,    4,    5,     6,  ...
%e A303484 1,  3,   6,   11,   20,    37,  ...
%e A303484 1,  4,  11,   30,   84,   237,  ...
%e A303484 1,  5,  18,   66,  241,   853,  ...
%e A303484 1,  6,  26,  115,  500,  2093,  ...
%t A303484 Table[Function[k, SeriesCoefficient[1/(1 - x) Sum[x^i^3, {i, 0, n}]^k, {x, 0, n^3}]][j - n], {j, 0, 11}, {n, 0, j}] // Flatten
%Y A303484 Columns k=0..4 give A000012, A000027, A224214, A224215.
%Y A303484 Main diagonal gives A303169.
%Y A303484 Cf. A290054, A302998.
%K A303484 nonn,tabl
%O A303484 0,5
%A A303484 _Ilya Gutkovskiy_, Apr 24 2018