Question: Question 3: The function f N x N-N is defined by if m 2 0, if m f(m, n) f(m, n-1) 0 and n-1 -m

Question 3: The function f N x N-N is defined by

Question 3: The function f N x N-N is defined by if m 2 0, if m f(m, n) f(m, n-1) 0 and n-1 -m . Solve this recurrence, i.e., express f(mm) in terms of m and n only. As always, prove that your answer is correct Question 4: In class, we have seen that for any integer m 2 1, the number of 00-free bitstrings of length m is equal to /m+2, which is the (m + 2)-th Fibonacci number. Let n 2 2 be an integer. For each of the following, justify your answer. How many 00-free bitstrings of length n do not contain any 0? How many 00-free bitstrings of length n have the following property: The rightmost 0 is at position 1 How many 00-free bitstrings of length n have the following property: The rightmost 0 is at position 2. . Let k be an integer with 3

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