[seqfan] Re: Generalized Pellian sequences

[Max Alekseyev]

Horadam sequence is a linear combination of Lucas sequences, namely:
H(n) = (b-a*p/2)*U_n(p,-q) + (a/2)*V_n(p,-q)
See http://en.wikipedia.org/wiki/Lucas_sequence

I would call all these sequences generalized Lucas.

Regards,
Max

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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