[seqfan] Re: Conjecture about A127750

[israel at math.ubc.ca]

You might upload a text file, or even better a nicely formatted .pdf 
(produced from Latex, for example), in the Links section of the sequence. 
If you want a more formal publication, you might send it to the Journal of 
Integer Sequences, and then include a link to that with the sequence (first 
to the ArXiv preprint, and eventually to the published article).

Cheers,
Robert

On Feb 9 2021, Allan Wechsler 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?
>> >
>> > --
>> > Seqfan Mailing list - http://list.seqfan.eu/
>> >
>>
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>
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