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  3. 4. [2 marks each] find the following recurrence re

4. [2 marks each] Find the following recurrence relations and give initial conditions, but DO...

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4. [2 marks each] Find the following recurrence relations and give initial conditions, but DO NOT SOLVE. (a) Let an,n0, be the number of n-character sequences of A 's, B 's, C 's, and D 's that contain exactly one A. Find a recurrence relation for an. (b) Let bn,n0, be the number of n-character sequences of 1s,2s,3s, and 4s that contain consecutive 1s somewhere in the sequence. Find a recurrence relation for bn. (c) Consider the set S={A,B,C,1,2,3,4}. For n0, let cn count the number of n-character sequences made by using elements from S that contain no consecutive letters (identical or distinct). For example, 23A3C4B is such a 7 -character sequence, but 1AA3B4C and AC23B4C are not. Find a recurrence relation for cn

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