Counting Strings: Consider the set of all strings of as, bs, and cs. a. Make a list of
Chapter 9, Problem 26(choose chapter or problem)
Counting Strings: Consider the set of all strings of a’s, b’s, and c’s.
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 \(s_{n}\) = the number of strings of a’s, b’s, and c’s of length n that do not contain the pattern aa. Find \(s_{0}, s_{1}, s_{2}, and s_{3}\).
c. Find a recurrence relation for \(s_{0}, s_{1}, s_{2}, . . .\).
d. Use the results of parts (b) and (c) to find the number of strings of a’s, b’s, and c’s of length four that do not contain the pattern aa.
e. Use the technique described in Section 5.8 to find an explicit formula for \(s_{0}, s_{1}, s_{2}, . . .\).
Text Transcription:
s_n
s_0, s_1, s_2, and s_3
s_0, s_1, s_2, . . .
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