A097542 a(n) = Sum_{k=1..2*n-1} J(4*n,k)*k, where J(i,j) is the Jacobi symbol.

1, -2, -4, 16, 0, -12, -16, 0, 54, -28, -28, 0, 0, -40, -48, 256, 0, -8, -76, 0, 0, -92, -80, 0, 500, -100, -4, 0, 0, -136, -160, 0, 0, -184, -152, 864, 0, -164, -208, 0, 0, -216, -252, 0, 0, -296, -224, 0, 2058, -12, -312, 0, 0, -12, -368, 0, 0, -396, -340, 0, 0, -336, 32, 4096, 0, -448, -492, 0, 0, -536, -464, 0, 0, -492

Offset

1,2

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..74.

Mathematica

Table[Sum[JacobiSymbol[4 n, k]*k, {k, 2*n - 1}], {n, 80}] (* Wesley Ivan Hurt, Feb 10 2026 *)

Crossrefs

Cf. A097542.

Sequence in context: A132483 A153064 A125594 * A277850 A332352 A217291

Adjacent sequences: A097539 A097540 A097541 * A097543 A097544 A097545

Keyword

sign

Author

N. J. A. Sloane, Aug 27 2004

Status

approved