A292118 G.f.: 1 + 2*Sum_{k >= 1} (-1)^k*q^A003159(k).

1, -2, 0, 2, -2, 2, 0, -2, 0, 2, 0, -2, 2, -2, 0, 2, -2, 2, 0, -2, 2, -2, 0, 2, 0, -2, 0, 2, -2, 2, 0, -2, 0, 2, 0, -2, 2, -2, 0, 2, 0, -2, 0, 2, -2, 2, 0, -2, 2, -2, 0, 2, -2, 2, 0, -2, 0, 2, 0, -2, 2, -2, 0, 2, -2, 2, 0, -2, 2, -2, 0, 2, 0, -2, 0, 2, -2

Offset

0,2

Links

Sean A. Irvine, Table of n, a(n) for n = 0..10000

George E. Andrews and David Newman, Binary Representations and Theta Functions, 2017.

Formula

Andrews-Newman (2017) give many properties of this series.

Mathematica

Join[{1}, Differences[(-1)^ThueMorse[Range[0, 100]]]] (* Paolo Xausa, Dec 18 2023 *)

Crossrefs

Cf. A003159, A292118.

First differences of A106400.

Sequence in context: A082054 A327276 A044943 * A277486 A102395 A127504

Adjacent sequences: A292115 A292116 A292117 * A292119 A292120 A292121

Keyword

sign

Author

N. J. A. Sloane, Sep 09 2017

Status

approved