[seqfan] Re: Generalized Pellian sequences

[Charles Greathouse]

Shannon
http://www.fq.math.ca/Scanned/16-2/shannon.pdf
seems to identify the two (Horadam = Pellian).

Charles Greathouse
Analyst/Programmer
Case Western Reserve University


On Wed, Apr 30, 2014 at 10:11 AM, <charliemath at optonline.net> wrote:

>    Horadam sequences may be defined as follows:  Given constants a, b, p
> and q, let H(0) = a, H(1) = b and for n>1, let H(n) = p*H(n-1) + q*H(n-2).
>
>    I know Pellian sequences are a subset of Horadam sequences.  What I’d
> like to know is the restrictions on a, b, p and q that define a Pellian
> sequence.  Are other sequences besides A000129 (the Pell numbers)
> considered Pellian? Or are they all, like A048654 and A048879, considered
> “generalized” Pellian?  Is there a consensus of opinion as to what is a
> generalized Pellian sequence?
>
> Thanks for your input.
>
> Charlie Marion
> Yorktown Heights NY
>
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