A298641 Number of partitions of n^3 into cubes > 1.

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

Offset: 0

Author

Ilya Gutkovskiy, Jan 24 2018

Keywords

• nonn

Examples

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

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

Crossrefs

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

Programs

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 *)

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