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A339369 Number of partitions of n into an odd number of cubes. 2
0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 2, 3, 2, 3, 2, 3, 2, 4, 2, 4, 3, 4, 3, 4, 4, 4, 4, 5, 4, 5, 4, 5, 4, 6, 4, 6, 5, 6, 5, 7, 6, 7, 6, 8, 6, 8, 7, 8, 8, 9, 8, 9, 9, 9, 9, 10, 10, 11, 10, 12, 10, 12, 11, 12, 12, 14, 12, 14, 13, 14 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,18

LINKS

Table of n, a(n) for n=0..85.

Index entries for sequences related to partitions

Index entries for sequences related to sums of cubes

FORMULA

G.f.: (1/2) * (Product_{k>=1} 1 / (1 - x^(k^3)) - Product_{k>=1} 1 / (1 + x^(k^3))).

a(n) = (A003108(n) - A292560(n)) / 2.

EXAMPLE

a(17) = 2 because we have [8, 8, 1] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1].

MATHEMATICA

nmax = 85; CoefficientList[Series[(1/2) (Product[1/(1 - x^(k^3)), {k, 1, Floor[nmax^(1/3)] + 1}] - Product[1/(1 + x^(k^3)), {k, 1, Floor[nmax^(1/3)] + 1}]), {x, 0, nmax}], x]

CROSSREFS

Cf. A000578, A003108, A027193, A292560, A339365, A339368.

Sequence in context: A127267 A268173 A008617 * A025824 A230037 A211262

Adjacent sequences:  A339366 A339367 A339368 * A339370 A339371 A339372

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Dec 01 2020

STATUS

approved

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Last modified August 2 01:19 EDT 2021. Contains 346408 sequences. (Running on oeis4.)