self Maths Puzzle

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 S2k, where k is an integer?

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The least number of jumps required to reach S without any backtracking is 3. if there is back tracking, the number of jumps required to reach S is always odd.
Whenever the number of jumps is even, there is no paths to reach S.
Since '2k' is even . S2k=0 (ans)
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