Counting Strings: Consider the set of all strings of as,

Chapter 9, Problem 9.109

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Counting Strings: Consider the set of all strings of as, bs, and cs. a. Make a list of all of these strings of lengths zero, one, two, and three that do not contain the pattern aa. b. For each integer n 0, let sn = the number of strings of as, bs, and cs of length n that do not contain the pattern aa. Find s0,s1,s2, ands3. c.H Find a recurrence relation for s0,s1,s2,... . d. Use the results of parts (b) and (c) to nd the number of strings of as, bs, and cs of length four that do not contain the pattern aa.

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