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A303904 Expansion of (1/(1 - x))*Product_{k>=1} (1 + x^(k^3)). 0
1, 2, 2, 2, 2, 2, 2, 2, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 6, 6, 6, 6, 6, 6, 6, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 10, 10, 10, 10, 10, 10, 10, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Partial sums of A279329.

LINKS

Table of n, a(n) for n=0..91.

Index entries for sequences related to partitions

Index entries for sequences related to sums of cubes

FORMULA

a(n) ~ exp(2^(7/4) * ((2^(1/3) - 1) * Gamma(1/3) * Zeta(4/3))^(3/4) * n^(1/4) / 3^(3/2)) * 3^(5/4) / (2^(15/8) * sqrt(Pi) * ((2^(1/3) - 1) * Gamma(1/3) * Zeta(4/3))^(3/8) * n^(1/8)). - Vaclav Kotesovec, May 04 2018

MAPLE

b:= proc(n, i) option remember; `if`(n<0, 0,

     `if`(n=0, 1, `if`(n>i^2*(i+1)^2/4, 0, (t->

       b(t, min(t, i-1)))(n-i^3)+b(n, i-1))))

    end:

a:= proc(n) option remember; `if`(n<0, 0,

       b(n, iroot(n, 3))+a(n-1))

    end:

seq(a(n), n=0..100);  # Alois P. Heinz, May 02 2018

MATHEMATICA

nmax = 91; CoefficientList[Series[1/(1 - x) Product[1 + x^k^3, {k, 1, Floor[nmax^(1/3) + 1]}], {x, 0, nmax}], x]

CROSSREFS

Cf. A000578, A003997, A036469, A038348, A248801, A279329, A302834.

Sequence in context: A025845 A029393 A275150 * A173021 A109703 A103375

Adjacent sequences:  A303901 A303902 A303903 * A303905 A303906 A303907

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, May 02 2018

STATUS

approved

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Last modified July 11 17:24 EDT 2020. Contains 335626 sequences. (Running on oeis4.)