A097543 Sum_{k=1..n-1} J(2*n,k)*k^2, where J(i,j) is the Jacobi symbol.

0, 1, 1, -8, 10, -24, 17, 84, 25, 24, 115, -144, 170, -224, 98, 32, 244, 654, 803, -560, 916, -616, -109, 96, -152, 312, 913, -1120, 2238, -1440, 2051, 5456, 1012, -272, 2438, -288, 1162, -2888, 2596, 96, 5864, 1008, 3315, -4048, 3840, -3680, -155, 576, 1713, 16700, 8838, -5200, 3166

Offset

1,4

Comments

Suggested by a formula in Petersson.

References

H. Petersson, Modulfunktionen und Quadratische Formen, Springer-Verlag, 1982; p. 98.

Links

Table of n, a(n) for n=1..53.

Mathematica

Table[Sum[JacobiSymbol[2n, k] k^2, {k, 1, n - 1}], {n, 50}] (* Alonso del Arte, Oct 24 2014 *)

Prog

(PARI) a(n)=sum(k=1, n-1, kronecker(2*n, k)*k^2); \\ Joerg Arndt, Oct 25 2014

Crossrefs

Cf. A097541-A097544.

Sequence in context: A032488 A102844 A303199 * A088034 A182405 A182366

Adjacent sequences: A097540 A097541 A097542 * A097544 A097545 A097546

Keyword

sign

Author

N. J. A. Sloane, Aug 27 2004

Status

approved