recursive functions question

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 = {f}, Si = {0,1}, S2 = {00, 01, 10, 11}, S3 = {000,001, 02,011, 100, 101, 110, 111} S4 = {0000, 0001, DOLO, 0011, 0100, 0181, 0110,0111, 1000, 1001, 1020, 1011, 1100, 1101, 1110, 1111} a. Argue that, for n >3, Sol = \S11 + 3S-6l +2. (1) 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? 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 = {f}, Si = {0,1}, S2 = {00, 01, 10, 11}, S3 = {000,001, 02,011, 100, 101, 110, 111} S4 = {0000, 0001, DOLO, 0011, 0100, 0181, 0110,0111, 1000, 1001, 1020, 1011, 1100, 1101, 1110, 1111} a. Argue that, for n >3, Sol = \S11 + 3S-6l +2. (1) 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