A354778 Number of integer quadruples (u,v,w,x) such that u^2+v^2+w^2+x^2 = n^2 and u+v+w+x = n.

1, 4, 8, 16, 8, 28, 32, 28, 8, 52, 56, 52, 32, 52, 56, 112, 8, 76, 104, 76, 56, 112, 104, 100, 32, 148, 104, 160, 56, 124, 224, 124, 8, 208, 152, 196, 104, 148, 152, 208, 56, 172, 224, 172, 104, 364, 200, 196, 32, 196, 296, 304, 104, 220, 320, 364, 56, 304, 248, 244, 224, 244, 248, 364, 8, 364, 416, 268, 152, 400, 392, 292, 104, 292, 296, 592, 152, 364, 416, 316, 56, 484, 344, 340, 224

Offset: 0

Author

N. J. A. Sloane, Jun 27 2022

Keywords

• nonn

Comments

This has the most natural offset, 0, just as A000118 does. A354766 gives one-quarter of a(n) for n > 0, and A278085 counts primitive solutions.

Crossrefs

a(n) = A354777(n^2,n).

Cf. A000118, A278085, A354766.

Formula

See A278085 and A354766 for some conjectural formulas.