\problemdata
{s01-ps7}
{counting}

\begin{problem} In Professor Karger's folk-dance class, dances are made of
four basic steps: a grapevine, a debka, a Yemenite, and a pivot.
There are some constraints:
\begin{itemize}
\item  A grapevine cannot follow a debka, and a debka cannot follow a
grapevine.  
\item A pivot cannot follow a Yemenite.  
\item Every dance must have at least one Yemenite
\end{itemize}
It \emph{is} permissible to repeat the same step multiple times, but
there must be at least 2 distinct steps in a dance.

How many distinct dances are there made up of a sequence of 5 basic
steps?
\end{problem}
