A) Find a recurrence relation for the number of bit strings of length n that contain a pair of consecutive 0s. b) What are the initial conditions?
c) How many bit strings of length seven contain two consecutive 0s?

A)

B)

C)   for n = 2

  = 1

for n = 3

  = 3

for n = 4

= 8

for n = 5

= 19

Step-by-step explanation:

A) A recurrence relation for the number of bit strings of length n that contain a  pair of consecutive Os can be represented below

if a string (n ) ends with 00 for n-2 positions there are a pair of  consecutive Os therefore there will be : strings

therefore for n ≥ 2

The recurrence relation for the number of bit strings of length 'n' that contains consecutive Os

b ) The initial conditions

The initial conditions are :

C) The number of bit strings of length seven containing two consecutive 0s

here we apply the re occurrence relation and the initial conditions

for n = 2

  = 1

for n = 3

  = 3

for n = 4

= 8

for n = 5

= 19

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