In the Name of GOD Discrete Mathematics th 6 Exercise, Deadline: 23rd Aban Computer Department at Sharif University of Tech. 1- A string that contains only 0s, 1s, and 2s is called a ternary string. a. Find e recurrence relation for the number of ternary strings that do not contain two consecutive 0s or two consecutive 1s. b. What are the initial conditions? c. How many ternary strings of length six do not contain two consecutive 0s or two consecutive 1s? 2- What is the general form of the particular solution of the linear nonhomogeneous recurrence relation if a. b. 3- Suppose that ( ) when is divisible by 5, and . Find . 4- For the following generating function find a closed formula for the sequence it determines. 5- What is the coefficient of in the power series of . 6- Use generating functions to solve the recurrence the relation initial conditions , . 7- How many bit strings of length eight do not contain six consecutive 0s? with
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