A225132 - OEIS

%I #9 Mar 24 2021 08:46:45

%S 1,-1,1,-2,3,-4,5,-8,12,-16,22,-32,45,-62,87,-124,175,-244,343,-484,

%T 679,-952,1339,-1884,2646,-3716,5224,-7342,10313,-14490,20365,-28618,

%U 40210,-56502,79400,-111570,156769,-220290,309553,-434974,611210,-858864,1206862

%N Convolutory inverse of the Thue Morse sequence.

%C 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... .

%H Clark Kimberling, <a href="/A225132/b225132.txt">Table of n, a(n) for n = 1..1000</a>

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

%t 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}]

%Y Cf. A030018, A010060.

%K sign

%O 1,4

%A _Clark Kimberling_, Apr 29 2013