Given the following definition, compute Q(5).

Question

   Q(n) = {0                                             if n = 0 

                1                                             if n=1

                3                                             if n=2

                Q(n − 1) + Q(n − 2) + Q(n − 3) if n > 2

Q(5)=__ans______________

Answer 1

5 > 2, therefore

Q(5) = Q(4) + Q(3) + Q(2)

4 > 2, therefore

Q(5) = Q(3) + Q(2) + Q(1) + Q(3) + Q(2)

3 > 2

Q(5) = Q(2) + Q(1) + Q(0) + Q(2) + Q(1) + Q(3) + Q(2)

 

Can you substitute and answer?