  The lattice path model suggested by E. Deutsch is derived from ordinary Dyck
paths, but with additional down-steps of size -3,-5,-7,... . For such paths, we
find the generating functions of them, according to length, ending at level
$i$, both, when considering them from left to right and from right to left. The
generating functions are intrinsically cubic, and thus (for $i=0$) in bijection
to various objects, like even trees, ternary trees, etc.
