  We give several bijections among restricted Motzkin paths, explaining why
various parameters on these paths are equidistributed. For example, the number
of doublerise-free Motzkin paths of length n is the same as the number of
peak-free Motzkin paths of length n+1 and the parameter "number of doublefalls"
has the same distribution on the former set as "number of valleys" does on the
latter. The bijections are most easily presented recursively but we also give
explicit descriptions using the notion of Motzkin tree.

Combinatorics