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Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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
Transcribed Image Text:Find a recurrence relation for the number of bit strings of length n that doesn't contain a pair of consecutive Os.
a) What are the initial conditions?
b) How many bit strings of length seven that doesn't contain two consecutive Os?
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- Consider the task of arranging red, white, and blue flags on an n-foot flagpole with no gaps, where red flags are 4- feet high, white flags are 2-feet high, and blue flags are 1-foot high. Which of the following recurrence relations can be used to determine the number distinct ways x(n) of arranging red, white, and blue flags on the n-foot flagpole for n=1,2,3, ... if the appropriate initial conditions are known? O x(n) = x(n-3) + x(n-2) + x(n-1), n = 5,6,7, .. O x(n) = 4x(n-4) + 2x(n-2) + x(n-1), n 5,6,7, . O x(n) = x(n-4) + x(n-2) + x(n-1), n = 5,6,7, .. O x(n+4) = x(n) + x(n-1) + x(n-2), n = 1,2,3, .. • Previous Next Simpfunarrow_forward(c) How many binary strings of length 5 have at least 2 adjacent bits that are the same (“00" or “11") somewhere in the string?arrow_forwardtn be the number of strings that are length n in {1, 2, 3} that don’t have 11 as a substring. What is the recurrence relation for tn?arrow_forward
- Let S be the set of all bit strings (strings of 0's and I's) Select one: O A. f(s) = the string obtained by moving the first bit of s to the end of the string. (For example, f(1001101) = 0011011) O B. f(s) = the string obtained from s by interchanging 0's and I's. (For example, f(11000) = 00111) O c. f(s) the string & with a 1 bit appended at the end. (For example, f(1101) = 11011) O D. f(s) the reversal of s. (For example, f(110) = 011) length at least 2. Which of the following functions f : S → S is not onto S?arrow_forward2. Let an be the number of ways to write the numbers 1, 2, 3, ..., n in order such that no number i appears immediately before i + 1 (this is a question which appeared on the exam, where an explicit formula was requested!). Explain why an will satisfy the recurrence an = (n-1) an-1+ (n − 2)an-2 for every n ≥ 2.arrow_forward
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