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A025457 Number of partitions of n into 4 positive cubes.

%I A025457 #32 Apr 23 2019 09:19:12
%S A025457 0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,
%T A025457 0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,1,
%U A025457 0,0,1,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1
%N A025457 Number of partitions of n into 4 positive cubes.
%C A025457 The first term > 1 is a(219) = 2. - _Michel Marcus_, Apr 23 2019
%H A025457 Robert Israel, <a href="/A025457/b025457.txt">Table of n, a(n) for n = 0..10000</a>
%H A025457 <a href="/index/Su#ssq">Index entries for sequences related to sums of cubes</a>
%F A025457 a(n) = [x^n y^4] Product_{k>=1} 1/(1 - y*x^(k^3)). - _Ilya Gutkovskiy_, Apr 23 2019
%p A025457 N:= 100;
%p A025457 A:= Array(0..N);
%p A025457 for a from 1 to floor(N^(1/3)) do
%p A025457   for b from a to floor((N-a^3)^(1/3)) do
%p A025457      for c from b to floor((N-a^3-b^3)^(1/3)) do
%p A025457         for d from c to floor((N-a^3-b^3-c^3)^(1/3)) do
%p A025457           n:= a^3 + b^3 + c^3 + d^3;
%p A025457           A[n]:= A[n]+1;
%p A025457 od od od od:
%p A025457 seq(A[n],n=0..N); # _Robert Israel_, Aug 18 2014
%p A025457 A025457 := proc(n)
%p A025457     local a,x,y,z,ucu ;
%p A025457     a := 0 ;
%p A025457     for x from 1 do
%p A025457         if 4*x^3 > n then
%p A025457             return a;
%p A025457         end if;
%p A025457         for y from x do
%p A025457             if x^3+3*y^3 > n then
%p A025457                 break;
%p A025457             end if;
%p A025457             for z from y do
%p A025457                 if x^3+y^3+2*z^3 > n then
%p A025457                     break;
%p A025457                 end if;
%p A025457                 ucu := n-x^3-y^3-z^3 ;
%p A025457                 if isA000578(ucu) then
%p A025457                     a := a+1 ;
%p A025457                 end if;
%p A025457             end do:
%p A025457         end do:
%p A025457     end do:
%p A025457 end proc: # _R. J. Mathar_, Sep 15 2015
%t A025457 r[n_] := Reduce[0 < a <= b <= c <= d && n == a^3+b^3+c^3+d^3, {a, b, c, d}, Integers];
%t A025457 a[n_] := Which[rn = r[n]; rn === False, 0, rn[[0]] === And, 1, rn[[0]] === Or, Length[rn], True, Print["error ", rn]];
%t A025457 Table[a[n], {n, 0, 107}] (* _Jean-François Alcover_, Feb 26 2019 *)
%Y A025457 Cf. A003108, A025455, A025456, A025403-A025407, A003327, A025420 (greedy inverse).
%K A025457 nonn
%O A025457 0,220
%A A025457 _David W. Wilson_
%E A025457 Second offset from _Michel Marcus_, Apr 23 2019