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

[David Scambler]

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

regards
dave