A303169 -id:A303169 - cp's OEIS frontend

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

Ilya Gutkovskiy, Apr 24 2018

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

			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,  ...

Index entries for sequences related to sums of cubes

Columns k=0..4 give A000012, A000027, A224214, A224215.
Main diagonal gives A303169.
Cf. A290054, A302998.

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

A303485 a(n) = [x^(n^3)] (1/(1 - x))*(Sum_{k>=1} x^(k^3))^n.

Original entry on oeis.org

1, 1, 1, 8, 66, 512, 5269, 57459, 711742, 9610222, 139735699, 2183555015, 36543300668, 649320343729, 12174674648730, 240360451018461, 4975239937954534, 107600744797471150, 2426579187889852885, 56901290353169050995, 1384258146777832889697

Offset: 0

Ilya Gutkovskiy, Apr 24 2018

nonn

Number of positive solutions to (x_1)^3 + (x_2)^3 + ... + (x_n)^3 <= n^3.

Index entries for sequences related to sums of cubes

Cf. A000578, A010057, A051344, A280618, A298672, A302995, A303169.

Join[{1}, Table[SeriesCoefficient[1/(1 - x) Sum[x^k^3, {k, 1, n}]^n, {x, 0, n^3}], {n, 20}]]

cp's OEIS Frontend

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.

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