$PQRSTU$ is a regular hexagon drawn on the ground. Prashant stands at $P$ and he starts jumping from vertex to vertex beginning from $P$. From any vertex of the hexagon except $S$, which is opposite to $A$, he may jump to any adjacent vertices. When he reaches $S$, he stops. Let Sn be the number of distinct paths of exactly $n$ jumps ending at $S$. What is the value of $S^2k$, where $k$ is an integer?
Depends on the value of $k$
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