[seqfan] Re: Dyck paths with no consecutive peaks/valleys at the same height

N. J. A. Sloane njas at research.att.com
Wed Nov 24 01:23:24 CET 2010


Dave, On Nov 8 you said:

>From: David Scambler <dscambler at bmm.com>
>To: "seqfan at list.seqfan.eu" <seqfan at list.seqfan.eu>
>Subject: [seqfan] Dyck paths with no consecutive peaks/valleys at the same  height

>If my counting is ok...

>A count of dyck paths of semi-length n with no consecutive valleys at the same height yields a(n) = 1,1,2,4,9,22,57,154,429,1223,
>which matches OEIS A105633<http://www.research.att.com/~njas/sequences/A105633>.

>Count of dyck paths of semi-length n with no consecutive peaks at the same height yields
>a(n) = 1,1,1,3,6,16,43,116,329,947,2762,8176,24469,73896,224960,689623,2126947,6595273... , not in OEIS

>Count of dyck paths of semi-length n with neither consecutive peaks at the same height nor consecutive valleys at the same height yields
>a(n) = 1,1,1,3,5,13,29,73,185,481,1263,3383,9135,24943,68613,190189,530379,1487439... , not in OEIS

In the old days I would have had to enter these myself - but now I can ask you
to do so, please!

Thanks

Neil





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