  In a paper by Sapounakis, Tasoulas, and Tsikouras \cite{stt}, the authors
count the number of occurrences of patterns of length four in Dyck paths. In
this paper we specify in one direction and generalize in another. We only count
ballot paths that avoid a given pattern, where a ballot path stays weakly above
the diagonal $y=x$, starts at the origin, and takes steps from the set
$\{\uparrow ,\to \}=\{u,r\}$. A pattern is a finite string made from the same
step set; it is also a path. Notice that a ballot path ending at a point along
the diagonal is a Dyck path.
