  We derive the length and area generating function of planar height-restricted
forward-moving discrete paths of increments +1, 0, or -1 with arbitrary
starting and ending points, the so-called Motzkin meanders, and the more
general length-area generating functions for Motzkin paths with markers
monitoring the number of passages from the two height boundaries ('floor' and
'ceiling') and the time spent there. The results are obtained by embedding
Motzkin paths in a two-step anisotropic Dyck path process and using propagator,
exclusion statistics and bosonization techniques. We also present a cluster
expansion of the logarithm of the generating functions that makes their
polynomial structure explicit. These results are relevant to the derivation of
statistical mechanical properties of physical systems such as polymers,
vesicles, and solid-on-solid interfaces.
