[seqfan] SIAM Rev problem 89-19

Richard Mathar mathar at strw.leidenuniv.nl
Tue Oct 18 00:15:08 CEST 2011

In problem  89-19 of SIAM Review vol 31 no 4 (1989) on page 676
a certain David W. Wilson orders:  "Find the MacLaurin series
expansion of F(x) that satisfies the funcional equation
(x^4-1)*F(x^4)+(x+1)*F(x^2)-x*F(x)=0, F(0)=a, F'(0)=b
This problem arose in a study of the acceptance of binary numerical
strings by finite automata."
I did not find any "solution" page on this question in the journal.
Are any of these series coefficients in the OEIS? Are they "interesting"?
The one that starts linearly, F(0)=0, F'(0)=1 seems to
have the Taylor coefficients 1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,...
(leading 0 from the absolute term omitted).



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