A229296 Number of solutions to x^2 + y^2 == n (mod 2*n) for x,y in [0, 2*n).

2, 4, 2, 8, 18, 4, 2, 16, 18, 36, 2, 8, 50, 4, 18, 32, 66, 36, 2, 72, 2, 4, 2, 16, 130, 100, 18, 8, 114, 36, 2, 64, 2, 132, 18, 72, 146, 4, 50, 144, 162, 4, 2, 8, 162, 4, 2, 32, 98, 260, 66, 200, 210, 36, 18, 16, 2, 228, 2, 72, 242, 4, 18, 128, 450, 4, 2

Offset: 1

Author

José María Grau Ribas, Sep 22 2013

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A086933, A229294, A229295, A229296, A229297.

Programs

Mathematica

A[n_] := Sum[If[Mod[a^2+b^2, 2n] == n, 1, 0], {a, 0, 2n - 1}, {b, 0, 2n - 1}]; Array[A, 100]

PARI

a(n)={my(m=2*n); my(p=Mod(sum(i=0, m-1, x^(i^2%m)), x^m-1)^2); polcoeff( lift(p), n)} \\ Andrew Howroyd, Aug 07 2018

Formula

a(n) = 2*A086933(n). - Andrew Howroyd, Aug 07 2018