OFFSET
1,4
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... .
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..1000
EXAMPLE
(1,1,0,1,0,0,1,1,...)**(1,-1,1,-2,3,-4,5,-8,...) = (1,0,0,0,0,...), where ** denotes convolution.
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}]
CROSSREFS
KEYWORD
sign
AUTHOR
Clark Kimberling, Apr 29 2013
STATUS
approved