%I #23 Dec 18 2023 08:28:15

%S 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,

%T 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,

%U -2,2,-2,0,2,-2,2,0,-2,2,-2,0,2,0,-2,0,2,-2

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

%H Sean A. Irvine, <a href="/A292118/b292118.txt">Table of n, a(n) for n = 0..10000</a>

%H George E. Andrews and David Newman, <a href="https://georgeandrews1.github.io/pdf/322.pdf">Binary Representations and Theta Functions</a>, 2017.

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

%t Join[{1},Differences[(-1)^ThueMorse[Range[0,100]]]] (* _Paolo Xausa_, Dec 18 2023 *)

%Y Cf. A003159, A292118.

%Y First differences of A106400.

%K sign

%O 0,2

%A _N. J. A. Sloane_, Sep 09 2017