[seqfan] Re: Concerning William Orrick's message

[William Orrick]

Dear Neil,

There was an error in my original "menage numbers" post, which I tried to
correct in a followup post, but I think the latter got overlooked.

The desymmetrized choice should have been 1, -1, 0 1, 2, 13, ..., the same
as the current A000179. I accidentally omitted the  second 1.  Just to be
clear, a(0) = 1, a(1) = -1, a(2) = 0, a(3) = 1 (not 2), a(4) = 2, a(5) = 13.

So there is no need for a new A335701.

Sorry for messing things up the first time.

I'd be happy to help with making sure all dependencies link to the correct
sequence once the new sequences are in place.

Best,
Will

On Thu, Aug 6, 2020 at 12:59 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"
>
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>