Question 14
Let $SP_1P_2P_3EP_4P_5$ be a heptagon. A frog starts jumping at vertex $S.$ From any vertex of the heptagon except $E,$ the frog may jump to either of the two adjacent vertices. When it reaches vertex $E,$ the frog stops and stays there. Find the number of distinct sequences of jumps of no more than $12$ jumps that end at $E.$