10. Suppose we let f(n) be the number of sequences of zeros and l's of length n that do not contain three consecutive 0's. Thus, f(1) = 2, f(2) = 4 and f(3) = 7. Prove that f(n+3) = f(n+2)+f(n+1) +f(n). Use this and a computer to compute f(100)- you must explain your calculational procedure.

Fig: 1