A225132 Convolutory inverse of the Thue Morse sequence.

1, -1, 1, -2, 3, -4, 5, -8, 12, -16, 22, -32, 45, -62, 87, -124, 175, -244, 343, -484, 679, -952, 1339, -1884, 2646, -3716, 5224, -7342, 10313, -14490, 20365, -28618, 40210, -56502, 79400, -111570, 156769, -220290, 309553, -434974, 611210, -858864, 1206862

Offset: 1

Author

Clark Kimberling, Apr 29 2013

Keywords

• sign

Comments

Coefficients in 1/(1+g(x)), where g is the generating function of the Thue-Morse sequence, A010060. Conjecture: a(n+1)/a(n) -> -1.405177106052... .

Examples

			(1,1,0,1,0,0,1,1,...)**(1,-1,1,-2,3,-4,5,-8,...) = (1,0,0,0,0,...), where ** denotes convolution.
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A030018, A010060.

Programs

Mathematica

r[n_] := If[n == 0, 0, If[Mod[n, 2] == 0, r[n/2], 1 - r[(n - 1)/2]]]; Table[r[n], {n, 1, 30}]; (* A010060 *) k[n_] := k[n] = 0; k[1] = 1; s[n_] := s[n] = (k[n] - Sum[r[k]*s[n - k + 1], {k, 2, n}])/r[1]; Table[s[n], {n, 1, 60}]