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A298641
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Number of partitions of n^3 into cubes > 1.
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6
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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
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OFFSET
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0,5
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LINKS
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FORMULA
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a(n) = [x^(n^3)] Product_{k>=2} 1/(1 - x^(k^3)).
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
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EXAMPLE
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a(4) = 2 because we have [64] and [8, 8, 8, 8, 8, 8, 8, 8].
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MAPLE
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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):
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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