[seqfan] Re: Periodicity of seqs mod m - research idea

Richard J. Mathar mathar at mpia-hd.mpg.de
Thu Feb 23 10:15:00 CET 2017


Related to http://list.seqfan.eu/pipermail/seqfan/2017-February/017289.html

What is the status for the D-finite sequences, where the coefficients
in the recurrence are polynomials of some (restricted) order? The linear
recurrences with constant coefficients obviously are a sub-family of these.
Given that polynomials p(n) have linear recurrences with constant
coefficients, does this trigger modular recurrences of sequences a(n) that
obey sum_i p_i(n) a(n-i) =0?
There is Hadamard's observation that the term-by-term product of
sequences with linear recurrences with constant coeffs is a sequence with 
linear recurrences with constant coeffs, so the Pisano periodicity
carries on. Does a "convolution" p_i(n)*a(n-i) lead to something similar?

RJM


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