how do you find the recurrence relation?

3 Runs of zeros A run of 0's in a binary string s of length at least s a substring s of s consisting only of O's, such that each end of the substring is either adjacent to a 1 or is also the end of the whole string s. For example, the string 101100 has two runs of O's, one of length 1 and one of length 2 and the string 000 has one run of 0's of length 3, namely the whole string itself. Let R(n) be the total number of runs of O's, taken over all binary strings of size n21 1. Give values for R(1) and R(2): R(2): 3 2. Provide a recurrence relation for R(n), n21 The recurrence relation found by listing first few n and R(n) is I, if n = 1. R(n) S otherwise. 3. Justify why your recurrence is correct. Solve your recurrence, to express R(n) as a function of n n/2 7l