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