5. Consider the set Sn of binary strings whose length is n and for which 010 does not appear as a consecutive substring. For example, So = {e}, Si = {0,1}, S2 = {00,01, 10, 11}, S3 = {000,001, 0%, 011, 100, 101, 110, 111} S4 = {0000, 0001, OBKT, 0011, 0100, 0165, 0110,0111, 1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111} a. Argue that, for n > 3, \Sn= Sn-11 +\Sn-kl +2. (1) k=3 b. Write a program to compute Sn for n=0,..., 20 and look up the resulting sequence in the Online Encyclopedia of Integer Sequences. What did you find