login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A298641 Number of partitions of n^3 into cubes > 1. 6
1, 0, 1, 1, 2, 1, 8, 6, 45, 100, 377, 1181, 4063, 13225, 45218, 150928, 511970, 1717140, 5777895, 19308880, 64360153, 213446697, 705095144, 2317573307, 7583418322, 24690176885, 80003762726, 257959340058, 827713115396, 2642967441892, 8398644246488 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..100

Index entries for sequences related to sums of cubes

Index entries for related partition-counting sequences

FORMULA

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

a(n) = A078128(A000578(n)).

a(n) ~ exp(4*(Gamma(1/3) * Zeta(4/3))^(3/4) * n^(3/4) / 3^(3/2)) * (Gamma(1/3) * Zeta(4/3))^(3/2) / (8 * 3^(5/2) * Pi^2 * n^6). - Vaclav Kotesovec, Jan 31 2018

EXAMPLE

a(4) = 2 because we have [64] and [8, 8, 8, 8, 8, 8, 8, 8].

MAPLE

g:= proc(n, L) # number of partitions of n into cubes > 1 and <= L

   option remember;

   local t, k;

   t:= 0;

   if n = 0 then return 1 fi;

   if n < 8 then return 0 fi;

   for k from 2 while k^3 <= min(n, L) do

     t:= t + procname(n-k^3, k^3)

   od

end proc:

f:= n -> g(n^3, n^3):

map(f, [$0..50]); # Robert Israel, Jan 24 2018

MATHEMATICA

mx = 30; s = Series[Product[1/(1 - x^(k^3)), {k, 2, mx}], {x, 0, mx^3}]; Table[ CoefficientList[s, x][[1 + n^3]], {n, 0, mx}] (* Robert G. Wilson v, Jan 24 2018 *)

CROSSREFS

Cf. A000578, A003108, A030272, A078128, A092362, A259792, A279329, A280130, A290247.

Sequence in context: A019816 A214562 A280757 * A293415 A197018 A082532

Adjacent sequences:  A298638 A298639 A298640 * A298642 A298643 A298644

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jan 24 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 5 12:47 EDT 2020. Contains 334840 sequences. (Running on oeis4.)