  This article deals with the enumeration of directed lattice walks on the
integers with any finite set of steps, starting at a given altitude $j$ and
ending at a given altitude $k$, with additional constraints such as, for
example, to never attain altitude $0$ in-between. We first discuss the case of
walks on the integers with steps $-h, \dots, -1, +1, \dots, +h$. The case $h=1$
is equivalent to the classical Dyck paths, for which many ways of getting
explicit formulas involving Catalan-like numbers are known. The case $h=2$
corresponds to "basketball" walks, which we treat in full detail. Then we move
on to the more general case of walks with any finite set of steps, also
allowing some weights/probabilities associated with each step. We show how a
method of wide applicability, the so-called "kernel method", leads to explicit
formulas for the number of walks of length $n$, for any $h$, in terms of nested
sums of binomials. We finally relate some special cases to other combinatorial
problems, or to problems arising in queuing theory.
