1. Consider the sequences made of the letters a, b, c, d, e. let yn be the number of such sequences of length n in which no three consecutive entries are all in the set {a,b}; that is to say, the sequences must not contain any instances of aaa, aab, aba, .... Find y1, 92, 93 and write a difference equation for yn+3 in terms of yn, yn+1, Yn+2. Hint: Write A = {a,b} and C = {c, d, e} and call good the strings that satisfy the requirements. Any good string of length n+3 must end in one of the following ways: with a C-letter, with exactly one A-letter, or with exactly two A-letters.
1. Consider the sequences made of the letters a, b, c, d, e. let yn be the number of such sequences of length n in which no three consecutive entries are all in the set {a,b}; that is to say, the sequences must not contain any instances of aaa, aab, aba, .... Find y1, 92, 93 and write a difference equation for yn+3 in terms of yn, yn+1, Yn+2. Hint: Write A = {a,b} and C = {c, d, e} and call good the strings that satisfy the requirements. Any good string of length n+3 must end in one of the following ways: with a C-letter, with exactly one A-letter, or with exactly two A-letters.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:1. Consider the sequences made of the letters a, b, c, d, e.
let yn be the number of such sequences of length n in which no three
consecutive entries are all in the set {a,b}; that is to say, the sequences
must not contain any instances of aaa, aab, aba, ....
Find y1, 92, 93 and write a difference equation for yn+3 in terms of yn, yn+1, Yn+2.
Hint: Write A = {a,b} and C = {c, d, e} and call good the strings that
satisfy the requirements. Any good string of length n+3 must end in one
of the following ways: with a C-letter, with exactly one A-letter, or with
exactly two A-letters.
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