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Make a list of all of these strings of lengths zero one two

Question: 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 s₀, s₁, s₂, and s₃.

c. Find a recurrence relation for s₀, s₁, s₂,....

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.

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Mathematics: Make a list of all of these strings of lengths zero one two

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