A374088 Number of ordered pairs (x,y) of positive integers such that x^2 + x*y + y^2 = n.

0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 1, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 1, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 1, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 4, 0, 2

Offset: 0

Author

Seiichi Manyama, Jun 28 2024

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A063725, A374089.

Programs

Python

from sympy.abc import x, y
from sympy.solvers.diophantine.diophantine import diop_quadratic
def A374088(n): return sum(1 for d in diop_quadratic(x*(x+y)+y**2-n) if d[0]>0 and d[1]>0) # Chai Wah Wu, Jun 28 2024