how many sequences of ‘s and ‘s of length are there that begin with a , end with a , contain no two consecutive ‘s, and contain no three consecutive ‘s?

how many sequences of ‘s and ‘s of length are there that begin with a , end with a , contain no two consecutive ‘s, and contain no three consecutive ‘s?

sequencemust appear exactly 2 or 3positionsdown the line. In this case, we start at position b and end at position 19. answer is 65positionsdown the line. Therefore, we must add aseriesof c’s and d’s to get 18. There are several ways to do this:arrangethem.arrangethem.Summingthe four cases gives 1+28+35+1 = 65