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A025456
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Number of partitions of n into 3 positive cubes.
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16
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0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0
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OFFSET
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0,252
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COMMENTS
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LINKS
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FORMULA
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a(n) = [x^n y^3] Product_{k>=1} 1/(1 - y*x^(k^3)). - Ilya Gutkovskiy, Apr 23 2019
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MAPLE
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local a, x, y, zcu ;
a := 0 ;
for x from 1 do
if 3*x^3 > n then
return a;
end if;
for y from x do
if x^3+2*y^3 > n then
break;
end if;
zcu := n-x^3-y^3 ;
if isA000578(zcu) then
a := a+1 ;
end if;
end do:
end do:
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MATHEMATICA
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a[n_] := Count[ PowersRepresentations[n, 3, 3], pr_List /; FreeQ[pr, 0]]; Table[a[n], {n, 0, 107}] (* Jean-François Alcover, Oct 31 2012 *)
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PROG
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(PARI) a(n)=sum(a=sqrtnint(n\3, 3), sqrtnint(n, 3), sum(b=1, a, my(C=n-a^3-b^3, c); ispower(C, 3, &c)&&0<c&&c<=b)) \\ Charles R Greathouse IV, Jun 26 2013
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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