A295848 Number of nonnegative solutions to (x,y,z) = 1 and x^2 + y^2 + z^2 = n.

0, 3, 3, 1, 0, 6, 3, 0, 0, 3, 6, 3, 0, 6, 6, 0, 0, 9, 3, 3, 0, 6, 3, 0, 0, 6, 12, 3, 0, 12, 6, 0, 0, 6, 9, 6, 0, 6, 9, 0, 0, 15, 6, 3, 0, 6, 6, 0, 0, 6, 12, 6, 0, 12, 9, 0, 0, 6, 6, 9, 0, 12, 12, 0, 0, 18, 12, 3, 0, 12, 6, 0, 0, 9, 18, 6, 0, 12, 6, 0, 0, 9, 9, 9

Offset: 0

Author

Seiichi Manyama, Nov 29 2017

Keywords

• nonn
• easy
• look

Comments

a(n)=0 for n in A047536. - Robert Israel, Nov 30 2017

Examples

			a(1) = 3;
(1,0,0) = 1 and 1^2 + 0^2 + 0^2 = 1.
(0,1,0) = 1 and 0^2 + 1^2 + 0^2 = 1.
(0,0,1) = 1 and 0^2 + 0^2 + 1^2 = 1.
a(2) = 3;
(1,1,0) = 1 and 1^2 + 1^2 + 0^2 = 2.
(1,0,1) = 1 and 1^2 + 0^2 + 1^2 = 2.
(0,1,1) = 1 and 0^2 + 1^2 + 1^2 = 2.
a(3) = 1;
(1,1,1) = 1 and 1^2 + 1^2 + 1^2 = 3.
a(5) = 6;
(2,1,0) = 1 and 2^2 + 1^2 + 0^2 = 5.
(2,0,1) = 1 and 2^2 + 0^2 + 1^2 = 5.
(1,2,0) = 1 and 1^2 + 2^2 + 0^2 = 5.
(1,0,2) = 1 and 1^2 + 0^2 + 2^2 = 5.
(0,2,1) = 1 and 0^2 + 2^2 + 1^2 = 5.
(0,1,2) = 1 and 0^2 + 1^2 + 2^2 = 5.
		

Links

• Robert Israel, Table of n, a(n) for n = 0..10000 (n=0..200 from Seiichi Manyama)

Crossrefs

Cf. A002102, A047536, A048240, A295819, A295849.

Programs

Maple

N:= 100:
V:= Array(0..N):
for x from 0 to floor(sqrt(N/3)) do
  for y from x to floor(sqrt((N-x^2)/2)) do
    for z from y to floor(sqrt(N-x^2-y^2)) do
      if igcd(x,y,z) = 1 then
        r:= x^2 + y^2 + z^2;
        m:= nops({x,y,z});
        if m=3 then V[r]:= V[r]+6
        elif m=2 then V[r]:= V[r]+3
        else V[r]:= V[r]+1
        fi
      fi
od od od:
convert(V,list); # Robert Israel, Nov 30 2017

Mathematica

f[n_] := Total[ Length@ Permutations@# & /@ Select[ PowersRepresentations[n, 3, 2], GCD[#[[1]], #[[2]], #[[3]]] == 1 &]]; Array[f, 90, 0] (* Robert G. Wilson v, Nov 30 2017 *)