A298935 Number of partitions of n^3 into distinct squares.

1, 1, 0, 0, 1, 5, 8, 40, 96, 297, 1269, 3456, 12839, 46691, 153111, 577167, 2054576, 7602937, 29000337, 110645967, 418889453, 1580667760, 6058528796, 23121913246, 89793473393, 350029321425, 1359919742613, 5340642744919, 20948242218543, 82505892314268

Offset: 0

Author

Ilya Gutkovskiy, Jan 29 2018

Keywords

• nonn

Examples

			a(5) = 5 because we have [121, 4], [100, 25], [100, 16, 9], [64, 36, 25] and [64, 36, 16, 9].
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..80
• Index entries for sequences related to sums of squares
• Index entries for related partition-counting sequences

Crossrefs

Cf. A000290, A000578, A030272, A030273, A033461, A037444, A218494, A298330, A298642, A298934.

Programs

Mathematica

Table[SeriesCoefficient[Product[1 + x^k^2, {k, 1, Floor[n^(3/2) + 1]}], {x, 0, n^3}], {n, 0, 29}]

Formula

a(n) = [x^(n^3)] Product_{k>=1} (1 + x^(k^2)).

a(n) = A033461(A000578(n)).