[seqfan] Re: Concerning William Orrick's message

[Neil Sloane]

Hmmm...

I'm inclined to think that when William Orrick said

>>> 3) A "desymmetrized" choice:
>>>
>>> 1, -1, 0, 2, 13, 80, 579, 4738, ...

this was a mistake, and he really meant to say

>>> 3) A "desymmetrized" choice:
>>>
>>> 1, -1, 0, 1, 2, 13, 80, 579, 4738, ...

which of course is A000179.

So I am just going to create one new sequence (A335700) not two.


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 Thu, Aug 6, 2020 at 1:59 PM Neil Sloane <njasloane at gmail.com> wrote:

>
> (I am starting a new thread, that one was already too long)
>
> In an earlier message in the thread, William Orrick said there are 3
> possibilities for the start of the sequence:
> >>> 1) The physically correct choice: there is one empty arrangement, no
>
> >>> 1, 0, 0, 1, 2, 13, 80, 579, 4738, ... This will be the new A335700
>
> >>> 2) The mathematically nicest choice: Touchard gives an expression for
> the ...
> >>>
> >>> 2, -1, 0, 1, 2, 13, 80, 579, 4738, ... This is A102761
> >>>
>
> >>> 3) A "desymmetrized" choice:
> >>>
> >>> 1, -1, 0, 2, 13, 80, 579, 4738, ...  This will be the new A335701
>
> Then there is the existing sequence A000179, which is a fourth candidate:
>
> 4)  1, -1, 0, 1, 2, 13, 80, 579, 4738, 43387, ... This is A000179
>
> I think the way to resolve this is to have all 4 sequences  in the OEIS
> with distinct  A-numbers.
>
> In his email, Will favors sequence 2), which is A102761. And A000179 has
> to stay because it has existed as an OEIS entry for about 50 years
>
> I am going to create two entries, for 1) and 3), which will be A335700 and
> A335701.
>
> They will say something like "alternative starts to A000179 and A102761"
>
>
>
>