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.

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, 84, 66, 26, 7, 1, 1, 8, 70, 237, 241, 115, 37, 8, 1, 1, 9, 135, 662, 853, 500, 200, 50, 9, 1, 1, 10, 264, 1780, 2847, 2093, 1012, 302, 63, 10, 1, 1, 11, 520, 4536, 9033, 8451, 4914, 1769, 441, 80, 11, 1

Offset: 0

Author

Ilya Gutkovskiy, Apr 24 2018

Keywords

• nonn
• tabl

Comments

A(n,k) is the number of nonnegative solutions to (x_1)^3 + (x_2)^3 + ... + (x_k)^3 <= n^3.

Examples

			Square array begins:
1,  1,   1,    1,    1,     1,  ...
1,  2,   3,    4,    5,     6,  ...
1,  3,   6,   11,   20,    37,  ...
1,  4,  11,   30,   84,   237,  ...
1,  5,  18,   66,  241,   853,  ...
1,  6,  26,  115,  500,  2093,  ...
		

Links

• Index entries for sequences related to sums of cubes

Crossrefs

Columns k=0..4 give A000012, A000027, A224214, A224215.

Main diagonal gives A303169.

Cf. A290054, A302998.

Programs

Mathematica

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