Counting Strings:a. Make a list of all bit strings of

Chapter 9, Problem 25E

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Problem 25E

Counting Strings:

a. Make a list of all bit strings of lengths zero, one, two, three, and four that do not contain the bit pattern 111.

b. For each integer n ≥ 0, let dn = the number of bit strings of length n that do not contain the bit pattern 111. Find d0, d1, d2, d3, and d4.

c. Find a recurrence relation for d0, d1, d2, …

d. Use the results of parts (b) and (c) to find the number of bit strings of length five that do not contain the pattern 111.

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