[seqfan] Re: Conjecture about A127750

[Neil Sloane]

Allan,  Good to hear that you've proved that.  I would say definitely add a
text file to the sequence, giving the file a title like "Proof that
A127750(n+1) = 2 * A001151(n) - A209229(n)"

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 Tue, Feb 9, 2021 at 11:59 AM Allan Wechsler <acwacw at gmail.com> wrote:

> I'm afraid I'm not familiar with Hilbert determinants and Cauchy
> determinants -- but I do have a proof of the stated conjecture, and am just
> wondering what to do with it. Even if stated tersely, it wouldn't fit
> comfortably in the sequence comments. Do I need to publish a brief paper to
> ArXiv and reference it? Or should I upload a text file to OEIS itself? My
> main theorem is that A127750(n+1) = 2 * A001151(N) - A209229(N), and the
> conjecture follows as an easy corollary.
>
> On Tue, Feb 9, 2021 at 12:41 AM Jean-Paul Allouche <
> jean-paul.allouche at imj-prg.fr> wrote:
>
> > Hi
> >
> > Is it conceivable that this determinant has an explicit form (à la
> Hilbert
> > determinant or à la Cauchy determinant)?
> > best
> > jean-paul
> >
> > Le mar. 9 févr. 2021 à 06:25, Allan Wechsler <acwacw at gmail.com> a écrit
> :
> >
> > > Recently I was investigating a combinatorial system (a simple Turing
> > > machine, in fact), and became curious about a sequence it was
> > displaying. I
> > > looked up the sequence on OEIS and found https://oeis.org/A127750,
> which
> > > matched perfectly.
> > >
> > > The description in the entry had absolutely nothing to do with my
> > > generating system. But there is a conjecture, apparently due to either
> > the
> > > author, Dr. Paul Barry, or to Neil Sloane -- the entry isn't entirely
> > > clear.
> > >
> > > Obviously I wanted to know if my sequence and Barry's were the same. I
> > was
> > > able to analyze my own sequence fairly easily, and the conjecture was
> > quite
> > > trivially true for my sequence. If I could prove the identity of the
> two
> > > sequences, I would have proven the conjecture.
> > >
> > > Well, now I think I have proven it. What should I do next?
> > >
> > > --
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> > >
> >
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>
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