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A298935 Number of partitions of n^3 into distinct squares. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 27 08:51 EST 2020. Contains 332301 sequences. (Running on oeis4.)