[seqfan] Re: Conjecture about A127750

[Allan Wechsler]

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?
> >
> > --
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
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