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A025456 Number of partitions of n into 3 positive cubes.

%I A025456 #44 Apr 24 2019 06:11:40
%S A025456 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,
%T A025456 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,
%U A025456 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
%N A025456 Number of partitions of n into 3 positive cubes.
%C A025456 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
%C A025456 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
%C A025456 The first term > 1 is a(251) = 2. - _Michel Marcus_, Apr 23 2019
%H A025456 Charles R Greathouse IV, <a href="/A025456/b025456.txt">Table of n, a(n) for n = 0..10000</a>
%H A025456 <a href="/index/Su#ssq">Index entries for sequences related to sums of cubes</a>
%F A025456 a(n) = [x^n y^3] Product_{k>=1} 1/(1 - y*x^(k^3)). - _Ilya Gutkovskiy_, Apr 23 2019
%p A025456 A025456 := proc(n)
%p A025456     local a,x,y,zcu ;
%p A025456     a := 0 ;
%p A025456     for x from 1 do
%p A025456         if 3*x^3 > n then
%p A025456             return a;
%p A025456         end if;
%p A025456         for y from x do
%p A025456             if x^3+2*y^3 > n then
%p A025456                 break;
%p A025456             end if;
%p A025456             zcu := n-x^3-y^3 ;
%p A025456             if isA000578(zcu) then
%p A025456                 a := a+1 ;
%p A025456             end if;
%p A025456         end do:
%p A025456     end do:
%p A025456 end proc: # _R. J. Mathar_, Sep 15 2015
%t A025456 a[n_] := Count[ PowersRepresentations[n, 3, 3], pr_List /; FreeQ[pr, 0]]; Table[a[n], {n, 0, 107}] (* _Jean-François Alcover_, Oct 31 2012 *)
%o A025456 (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
%Y A025456 Least inverses are A025418.
%Y A025456 Cf. A025455, A003108, A003072 (1 or more ways), A008917 (two or more ways), A025395-A025398.
%K A025456 nonn
%O A025456 0,252
%A A025456 _David W. Wilson_
%E A025456 Second offset from _Michel Marcus_, Apr 23 2019