[seqfan] A005700 Number of Dyck paths: a(n) = <not a Dyck path>
dscambler at bmm.com
Fri Jan 28 05:46:28 CET 2011
"A005700 Number of Dyck paths: a(n) = number of walks of 2n unit steps north,
east, south, or west starting and ending at the origin and confined to the first octant."
It seems to me that the phrase "Dyck paths" immediately followed by a definition
that is not the definition of a Dyck path is invalid.
The definition is that of a closed first octant path, not a Dyck path.
At best, the references refer to pairs of Dyck paths.
To be sure there are generalizations of Dyck paths, but these are clearly distinguished by their names, e.g.
"grand Dyck path", "Dyck path of knight moves" etc.
Maybe "Number of lattice paths" would be better.
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