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ABCDEFGH is a regular octagon. A and E are opposite vertices of the octagon. A frog starts jumping from vertex to vertex, beginning from A. From any vertex of the octagon except E, it may jump to either of the two adjacent vertices. When it reaches E, the frog stops and stays there. Let an be the number of distinct paths of exactly n jumps ending in E. Then what is the value of $a_{2n – 1}$? 

  1. Zero 
  2. Four
  3. $2n – 1 $
  4. Cannot be determined
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