A342682 a(1) = 1; for n > 0: a(2*n) = -a(n+1), a(2*n+1) = a(n) + a(n+1).

1, 0, 1, -1, 1, 1, 0, -1, 0, -1, 2, 0, 1, 1, -1, 0, -1, 1, -1, -2, 1, 0, 2, -1, 1, -1, 2, 1, 0, 0, -1, 1, -1, -1, 0, 1, 0, 2, -3, -1, -1, 0, 1, -2, 2, 1, 1, -1, 0, 1, 0, -2, 1, -1, 3, 0, 1, 0, 0, 1, -1, -1, 0, 1, 0, 1, -2, 0, -1, -1, 1, 0, 1, -2, 2, 3, -1, 1, -4

Offset: 1

Author

George Beck, May 18 2021

Keywords

• sign

Examples

			a(2) = -a(2), so a(2) = 0; a(11) = a(5) + a(6) = 1 + 1 = 2.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000
• George Beck and Karl Dilcher, A Matrix Related to Stern Polynomials and the Prouhet-Thue-Morse Sequence, arXiv:2106.10400 [math.CO], 2021.

Crossrefs

Cf. A002487, A213369, A082498.

Programs

Mathematica

a@1 = 1;
a@2 = 0;
a@n_ := -a[n/2 + 1] /; EvenQ@n;
a@n_ := a[1/2 (n - 1)] + a[1/2 (n - 1) + 1] /; OddQ@n;
a /@ Range[128]