[seqfan] Re: a last-minute entry for the A200000 race

Rainer Rosenthal r.rosenthal at web.de
Wed Nov 23 13:24:33 CET 2011

On 23.11.2011 05:24, Jon Wild wrote:

> On Mon, 21 Nov 2011, Benoît Jubin wrote:
>> Write T(n,k) for the sequence of meanders on an (n,k)-grid and S(n,k)
>> for the same up to symmetry, that is,
>> S(n,k) <= T(n,k) <= (4 or 8)*S(n,k)
>> depending on whether n and k are equal or different (and the second
>> inequality gets asymptotically closer to an equality).

> I just adjusted my program to enumerate meanders on an (n,k) grid. Using 
> your nomenclature, I found that T(n,3) is given by A078008, the expansion 
> of (1-x)/(1-x-2*x^2). (I'll add a comment to A078008.) And this is 
> interesting: S(n,3) is given by A090597, which "arises from a conjecture 
> about sequence of rational links with n crossings". (I'll add a comment 
> here, too.)

Thanks for having that lovely new sequence as A200000.
It's not only a sequence, but it already has a story.
And that story is going to continue, I believe.

All the best and hooray 200000,

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