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

0,6

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

Formula

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

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

Example

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

Mathematica

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

Crossrefs

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

Sequence in context: A176757 A280965 A151349 * A258786 A192272 A073930

Adjacent sequences: A298932 A298933 A298934 * A298936 A298937 A298938

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 29 2018

Status

approved