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A298934 Number of partitions of n^2 into distinct cubes. 4
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 (list; graph; refs; listen; history; text; internal format)
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: A239927 A069846 A239657 * A309061 A289618 A161520

Adjacent sequences:  A298931 A298932 A298933 * A298935 A298936 A298937

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jan 29 2018

STATUS

approved

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Last modified February 17 23:35 EST 2020. Contains 332006 sequences. (Running on oeis4.)