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

Author

N. J. A. Sloane, Sep 09 2017

Keywords

• sign

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.

Crossrefs

Cf. A003159, A292118.

First differences of A106400.

Programs

Mathematica

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

Formula

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