[seqfan] Re: Continued Fractions

[Melvin M Peralta]

I seem to have made an error with the denominator sequence; it's the exact
same as the numerator sequence but with an extra 1 in front so probably no
need to create a separate entry.

But will add the comments nonetheless.

On Mon, Feb 22, 2016 at 9:16 AM, Neil Sloane <njasloane at gmail.com> wrote:

> Melvin, Please add a comment to A058182, and also submit the denominator
> sequence.  Nice question!
>
> I added a ref to the "Proofs" book, but maybe you could fill in the page
> number.
>
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
>
> On Sun, Feb 21, 2016 at 2:04 AM, Melvin M Peralta <
> melvinmperalta at gmail.com>
> wrote:
>
> > Hello SeqFans,
> >
> > a(0) = 1
> > a(n+1) = numerator of the simplified continued fraction resulting from
> > [a(0), a(1), ..., a(n)]
> >
> > 1, 1, 2, 5, 27, 734, 538783, ...
> >
> > a(n) is also the number of ways to tile an n-board with dominos and
> > stackable squares, where nothing can be stacked on a domino but
> > otherwise the i-th cell may be stacked by as many as a_i squares. (a nice
> > proof of this is given in "Proofs That Really Count").
> >
> > *My question*: From n>=2, the sequence appears identical to
> > https://oeis.org/A058182. Does it always coincide? If so is the
> connection
> > already implicit in the entry? Or should a comment be made?
> >
> > Note a similar sequence does not appear in OEIS:
> > a(0) = 1
> > a(n+1) = denominator of the simplified continued fraction resulting from
> > [a(0), a(1), ..., a(n)]
> >
> > 1, 1, 2, 3, 10, 103, 10619, ...
> >
> > This is also nice because a(n+1) is the number of ways to tile an n-board
> > in the same way described, except the first cell should be ignored
> > entirely.
> >
> > Best Regards,
> > Melvin
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>



-- 
Melvin M. Peralta
440.391.0073