A298936 Number of ordered ways of writing n^2 as a sum of n nonnegative cubes.

1, 1, 0, 6, 6, 20, 120, 7, 1689, 6636, 36540, 64020, 963996, 2894892, 19555965, 176079995, 955611188, 6684303780, 42462792168, 292378003753, 1886275214112, 13384059605364, 87399249887334, 624073002367892, 5080120229014734, 37587589611771480

Offset

0,4

Links

Table of n, a(n) for n=0..25.

Index entries for sequences related to sums of cubes

Formula

a(n) = [x^(n^2)] (Sum_{k>=0} x^(k^3))^n.

Example

a(3) = 6 because we have [8, 1, 0], [8, 0, 1], [1, 8, 0], [1, 0, 8], [0, 8, 1] and [0, 1, 8].

Maple

f:= n -> coeff(add(x^(k^3), k=0..floor(n^(2/3)))^n, x, n^2):
map(f, [$0..30]); # Robert Israel, Jan 29 2018

Mathematica

Table[SeriesCoefficient[Sum[x^k^3, {k, 0, Floor[n^(2/3) + 1]}]^n, {x, 0, n^2}], {n, 0, 25}]

Crossrefs

Cf. A000290, A000578, A023358, A030272, A218495, A259792, A291700, A298671, A298672, A298934, A298937.

Sequence in context: A309122 A115046 A004983 * A034695 A339338 A198340

Adjacent sequences: A298933 A298934 A298935 * A298937 A298938 A298939

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 29 2018

Status

approved