[seqfan] Re: Conjectures stated in Clark Kimberling's A192750

Richard J. Mathar mathar at mpia-hd.mpg.de
Wed Dec 16 16:27:23 CET 2015


Concerning: http://list.seqfan.eu/pipermail/seqfan/2015-December/015852.html

njas> A192750 has one clearly labeled conjecture, and two other formulas which
njas> were not labeled as conjectures, but probably were.

If we insert the expression of d_n into the recurrence for c_n and
vice versa, we get two "inhomogeneous" recurrences for d_n and
for c_n, where the additional terms are polynomials in the index.
This falls clearly into the realm of formulas for generating
functions with rational polynomials, because the generating
function of the extra term is already a rational polynomial.
See Eq. (4) in 
http://www.mpia.de/~mathar/public/mathar20071126.pdf

>From there the only remaining task is to find the few coefficients
in numerator and denominator of the generating function.

The Grunewald formulas look like just the Binet-formulas
associated with these.

Richard Mathar


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