A374092 Number of solutions to n = x^2 + x*y + y^2 with 0 < x < y.

0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1

Offset: 0

Author

Seiichi Manyama, Jun 28 2024

Keywords

• nonn

Comments

a(n) = 0 if n == 2 (mod 4). - Robert Israel, Jun 28 2024

Crossrefs

Cf. A025441, A374093, A374094.

Programs

Maple

N:= 200: # for a(0) .. a(N)
V:= Array(0..N):
for x from 1 to floor(sqrt(N/3)) do
  for y from x+1 do
     v:= x^2 + x*y + y^2;
     if v > N then break fi;
     V[v]:= V[v]+1;
od od:
convert(V,list); # Robert Israel, Jun 28 2024