A097536 -Sum_{k=1..2*q-1} J(k,q)*J(-4,k)*k/4 as q runs through numbers == 3 (mod 4), where J(i,j) is the Jacobi symbol.

1, 4, 7, 12, 19, 20, 1, 40, 38, 52, 63, 56, 78, 92, 85, -8, 123, 116, 6, 168, 129, 156, 206, 172, 28, 228, 197, 244, 278, 248, 270, 320, 279, 12, 381, 292, 8, 444, 364, 420, 467, 364, -38, 24, 471, 492, 550, 520, 540, 660, 508, 80, 737, 556, 692, 720, 575, 744, 846, 712, 1

Offset

1,2

Comments

Suggested by a formula in Petersson.

References

H. Petersson, Modulfunktionen und Quadratische Formen, Springer-Verlag, 1982; p. 103.

Links

Table of n, a(n) for n=1..61.

Maple

with(numtheory); J:=jacobi; f:=proc(q) add( J(k, q)*J(-4, k)*k, k=1..2*q-1); (-1)*(%/4); end;

Crossrefs

Cf. A097537.

Sequence in context: A265431 A132297 A007333 * A293829 A344421 A022809

Adjacent sequences: A097533 A097534 A097535 * A097537 A097538 A097539

Keyword

sign

Author

N. J. A. Sloane, Aug 27 2004

Status

approved