A290054 Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of (Sum_{j>=0} x^(j^3))^k.

1, 1, 0, 1, 1, 0, 1, 2, 0, 0, 1, 3, 1, 0, 0, 1, 4, 3, 0, 0, 0, 1, 5, 6, 1, 0, 0, 0, 1, 6, 10, 4, 0, 0, 0, 0, 1, 7, 15, 10, 1, 0, 0, 0, 0, 1, 8, 21, 20, 5, 0, 0, 0, 1, 0, 1, 9, 28, 35, 15, 1, 0, 0, 2, 0, 0, 1, 10, 36, 56, 35, 6, 0, 0, 3, 2, 0, 0, 1, 11, 45, 84, 70, 21, 1, 0, 4, 6, 0, 0, 0

Offset

0,8

Comments

A(n,k) is the number of ways of writing n as a sum of k nonnegative cubes.

Links

Seiichi Manyama, Antidiagonals n = 0..139, flattened

Index entries for sequences related to sums of cubes

Formula

G.f. of column k: (Sum_{j>=0} x^(j^3))^k.

Example

Square array begins:
1,  1,  1,  1,  1,   1,  ...
0,  1,  2,  3,  4,   5,  ...
0,  0,  1,  3,  6,  10,  ...
0,  0,  0,  1,  4,  10,  ...
0,  0,  0,  0,  1,   5,  ...
0,  0,  0,  0,  0,   1,  ...

Mathematica

Table[Function[k, SeriesCoefficient[Sum[x^i^3, {i, 0, n}]^k, {x, 0, n}]][j - n], {j, 0, 12}, {n, 0, j}] // Flatten

Crossrefs

Columns k=0-9 give: A000007, A010057, A173677, A051343, A173678, A173679, A173680, A173676, A173681, A173682.

Main diagonal gives A291700.

Antidiagonal sums give A302019.

Cf. A045847, A122141, A286815.

Sequence in context: A325466 A077029 A052553 * A290430 A290429 A045847

Adjacent sequences: A290051 A290052 A290053 * A290055 A290056 A290057

Keyword

nonn,tabl

Author

Ilya Gutkovskiy, Jul 19 2017

Status

approved