Eisenstein-Fibonacci sequences

[Max A.]

On 11/7/06, Joerg Arndt <arndt at jjj.de> wrote:
> * Jonathan Post <jvospost3 at gmail.com> [Nov 08. 2006 13:29]:
> > Thank you, Joerg.  That was interesting.  Does your generating function
> > hypothesis hold when I extend the sequence by another 5 values, to a(n) = 0, 0,
> > 1, 1, 3, 1, 7, 4,
> > 14, 17, 28, 54, 66, 143, 182, 350, 687, 987, 2611, 4298 ? Again, assuming that
> > I got the elementary algebra and arithmetic correct.
>
> Alas, the function I gave was spurious, with the
> additional terms no OGF is found.

Not surprising at all!
This sequence is not well-defined (see above in this discussion), so
one may view its terms as random numbers. How can they have an OGF? ;)

Max