A298934 Number of partitions of n^2 into distinct cubes.

1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 3, 1, 0, 0, 0, 0, 0, 0, 3, 3, 1, 0, 3, 0, 2, 4, 0, 0, 1, 0, 0, 2, 3, 1, 1, 0, 6, 3, 6, 1, 6, 0, 3, 9, 0, 6, 6, 7, 0, 10, 3, 3, 6, 0, 8, 6, 13, 2, 10, 9, 10, 19, 2, 14, 21, 7, 2, 25

Offset

0,16

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Index entries for sequences related to sums of cubes

Index entries for related partition-counting sequences

Formula

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

a(n) = A279329(A000290(n)).

Example

a(15) = 2 because we have [216, 8, 1] and [125, 64, 27, 8, 1].

Maple

b:= proc(n, i) option remember; `if`(n=0, 1,
      `if`(n>i^2*(i+1)^2/4, 0, b(n, i-1)+
      `if`(i^3>n, 0, b(n-i^3, i-1))))
    end:
a:= n-> b(n^2, n):
seq(a(n), n=0..100);  # Alois P. Heinz, Jan 29 2018

Mathematica

Table[SeriesCoefficient[Product[1 + x^k^3, {k, 1, Floor[n^(2/3) + 1]}], {x, 0, n^2}], {n, 0, 84}]

Crossrefs

Cf. A000290, A000578, A030272, A030273, A218495, A259792, A279329, A298672, A298848, A298935.

Sequence in context: A069846 A374092 A239657 * A309061 A289618 A161520

Adjacent sequences: A298931 A298932 A298933 * A298935 A298936 A298937

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 29 2018

Status

approved