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A025456
Number of partitions of n into 3 positive cubes.
16
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
OFFSET
0,252
COMMENTS
If A025455(n) > 0 then a(n + k^3) > 0 for k>0; a(A119977(n))>0; a(A003072(n))>0. - Reinhard Zumkeller, Jun 03 2006
a(A057904(n))=0; a(A003072(n))>0; a(A025395(n))=1; a(A008917(n))>1; a(A025396(n))=2. - Reinhard Zumkeller, Apr 23 2009
The first term > 1 is a(251) = 2. - Michel Marcus, Apr 23 2019
FORMULA
a(n) = [x^n y^3] Product_{k>=1} 1/(1 - y*x^(k^3)). - Ilya Gutkovskiy, Apr 23 2019
MAPLE
A025456 := proc(n)
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:
end proc: # R. J. Mathar, Sep 15 2015
MATHEMATICA
a[n_] := Count[ PowersRepresentations[n, 3, 3], pr_List /; FreeQ[pr, 0]]; Table[a[n], {n, 0, 107}] (* Jean-François Alcover, Oct 31 2012 *)
PROG
(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
CROSSREFS
Least inverses are A025418.
Cf. A025455, A003108, A003072 (1 or more ways), A008917 (two or more ways), A025395-A025398.
Sequence in context: A328981 A369070 A024360 * A288314 A285963 A024889
KEYWORD
nonn
EXTENSIONS
Second offset from Michel Marcus, Apr 23 2019
STATUS
approved