[seqfan] Re: A005043 - bijection sought
dscambler at bmm.com
Wed Apr 18 01:42:53 CEST 2012
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.
> 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?
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