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16 15. Let n be a positive integer. Recall that a string of length n using digits 0, 1, 2, 3 is a (ordered) sequence containing any n of the digits 0, 1, 2, 3. We write the sequence without the commas between the individual digits. For each nonnegative integer n, let = the number of strings of length n using digits 0, 1, 2, 3 which do not contain the pattern 00. Find a recurrence relation, including the initial conditions, for the sequence so, s1, $2, $3, Hint: The string 2010 is of length 4 and counted in sa. The string 2001 is not counted in $4 since it contains the pattern 00.

16 15. Let n be a positive integer. Recall that a string of length n using digits 0, 1, 2, 3 is a (ordered) sequence containing any n of the digits 0, 1, 2, 3. We write the sequence without the commas between the individual digits. For each nonnegative integer n, let = the number of strings of length n using digits 0, 1, 2, 3 which do not contain the pattern 00. Find a recurrence relation, including the initial conditions, for the sequence so, s1, $2, $3, Hint: The string 2010 is of length 4 and counted in sa. The string 2001 is not counted in $4 since it contains the pattern 00.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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16 15. Let n be a positive integer. Recall that a string of length n using digits 0, 1, 2, 3 is a (ordered) sequence containing any n of the digits 0, 1, 2, 3. We write the sequence without the commas between the individual digits. For each nonnegative integer n, let s = the number of strings of length n using digits 0, 1, 2, 3 which do not contain the pattern 00. Find a recurrence relation, including the initial conditions, for the sequence so, $1, $2, $3, Hìnt: The string 2010 is of length 4 and counted in sa. The string 2001 is not counted in $4 since it contains the pattern 00.
Transcribed Image Text:16 15. Let n be a positive integer. Recall that a string of length n using digits 0, 1, 2, 3 is a (ordered) sequence containing any n of the digits 0, 1, 2, 3. We write the sequence without the commas between the individual digits. For each nonnegative integer n, let s = the number of strings of length n using digits 0, 1, 2, 3 which do not contain the pattern 00. Find a recurrence relation, including the initial conditions, for the sequence so, $1, $2, $3, Hìnt: The string 2010 is of length 4 and counted in sa. The string 2001 is not counted in $4 since it contains the pattern 00.
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