A025456 - OEIS

%I #44 Apr 24 2019 06:11:40

%S 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 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 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 Number of partitions of n into 3 positive cubes.

%C 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 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 The first term > 1 is a(251) = 2. - _Michel Marcus_, Apr 23 2019

%H Charles R Greathouse IV, <a href="/A025456/b025456.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Su#ssq">Index entries for sequences related to sums of cubes</a>

%F a(n) = [x^n y^3] Product_{k>=1} 1/(1 - y*x^(k^3)). - _Ilya Gutkovskiy_, Apr 23 2019

%p A025456 := proc(n)

%p     local a,x,y,zcu ;

%p     a := 0 ;

%p     for x from 1 do

%p         if 3*x^3 > n then

%p             return a;

%p         end if;

%p         for y from x do

%p             if x^3+2*y^3 > n then

%p                 break;

%p             end if;

%p             zcu := n-x^3-y^3 ;

%p             if isA000578(zcu) then

%p                 a := a+1 ;

%p             end if;

%p         end do:

%p     end do:

%p end proc: # _R. J. Mathar_, Sep 15 2015

%t 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 (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 Least inverses are A025418.

%Y Cf. A025455, A003108, A003072 (1 or more ways), A008917 (two or more ways), A025395-A025398.

%K nonn

%O 0,252

%A _David W. Wilson_

%E Second offset from _Michel Marcus_, Apr 23 2019