A112347 Kronecker symbol (-1, n) except a(0) = 0.

0, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1

Offset

0,1

Links

Table of n, a(n) for n=0..102.

J.-P. Allouche and J. Shallit, On three conjectures of P. Barry, arxiv preprint arXiv:2006.04708 [math.NT], June 8 2020.

Paul Barry, Some observations on the Rueppel sequence and associated Hankel determinants, arXiv:2005.04066 [math.CO], 2020.

Index entries for sequences obtained by enumerating foldings

Formula

Multiplicative with a(2^e) = 1, a(p^e) = (-1)^(e(p-1)/2) if p>2.

a(2n) = a(n), a(4*n + 1) = 1, a(4*n + 3) = -1. a(-n) = -a(n).

a(n) = A034947(n) unless n=0.

Example

x + x^2 - x^3 + x^4 + x^5 - x^6 - x^7 + x^8 + x^9 + x^10 - x^11 - x^12 + x^13 + ...

Mathematica

Join[{0}, KroneckerSymbol[-1, Range[110]]] (* Harvey P. Dale, Jun 02 2019 *)

Prog

(PARI) {a(n) = if( n, kronecker( -1, n))}

Crossrefs

Cf. A034947.

First differences of A005811.

Sequence in context: A070238 A062157 A103131 * A057427 A178334 A000007

Adjacent sequences: A112344 A112345 A112346 * A112348 A112349 A112350

Keyword

sign,mult

Author

Michael Somos, Sep 12 2005

Status

approved