[seqfan] Re: A005043 - bijection sought

[David Scambler]

Let me clarify,

I refer to paths of semilength 2n and ascents and descents of exactly length 2. 

e.g. n=2, semilength = 4, total length = 8.

UUDUUDDD  2 up, 1 down, 2 up, 3 down. Ascents are length 2; descents are length 1 and 3 respectively. 

Empirically the counts match A005043 up to a(12) = 4213, if I am not mistaken.

dave

> What do you mena by "no descent of length 2"?
>
> You get always a descent of length 2 at the end 
> (except for such a path of length 0).
>
> Roland Bacher
>
> On Tue, Apr 17, 2012 at 12:21:11AM -0500, David Scambler wrote:
> Empirically, the following seems to be counted by A005043 ( https://oeis.org/A005043 )
> 
> Dyck 2n-paths with all ascents length 2 and no descents length 2.
> 
> Proof anyone?
> 
> dave