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Kenneth Rosen Edition 7 Exercise 8.1 Question 18 (Page No. 511)
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Find a recurrence relation for the number of ternary strings of length $n$ that contain two consecutive symbols that are the same.
What are the initial conditions?
How many ternary strings of length six contain consecutive symbols that are the same?
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Kenneth Rosen Edition 7 Exercise 8.1 Question 25 (Page No. 511)
How many bit sequences of length seven contain an even number of $0s?$
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Kenneth Rosen Edition 7 Exercise 8.1 Question 24 (Page No. 511)
Find a recurrence relation for the number of bit sequences of length $n$ with an even number of $0s.$
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Kenneth Rosen Edition 7 Exercise 8.1 Question 23 (Page No. 511)
Find the recurrence relation satisfied by $S_{n},$ where $S_{n}$ is the number of regions into which three-dimensional space is divided by $n$ planes if every three of the planes meet in one point, but no four of the planes go through the same point. Find $S_{n}$ using iteration.
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Kenneth Rosen Edition 7 Exercise 8.1 Question 22 (Page No. 511)
a) Find the recurrence relation satisfied by $R_{n},$ where $R_{n}$ is the number of regions into which the surface of a sphere is divided by $n$ great circles (which are the intersections of the sphere and planes passing through ... sphere), if no three of the great circles go through the same point. b) Find $R_{n}$ using iteration.
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