Need help with this problem. It states: Determine the number of n-digit quaternary (0, 1, 2, 3) sequences (in closed form) where there is never a 3 anywhere to the right of a 0. My current solution: I split it up into two parts, one for if there is a 0 in the sequence and one without. I've gathered that there are 3^(n-1) possibilities if the first digit is a 0 and you add it with the remaining which is 3^n? But something seems missing. Please help!!! Also how should I set up my characteristic polynomial? (S(k))? I have S(k) = S(k-1) + k*3S(k-1) and trying to solve for the coefficients. But it doesn't seem to be quite right. Please help and thank you!
Need help with this problem. It states: Determine the number of n-digit quaternary (0, 1, 2, 3) sequences (in closed form) where there is never a 3 anywhere to the right of a 0. My current solution: I split it up into two parts, one for if there is a 0 in the sequence and one without. I've gathered that there are 3^(n-1) possibilities if the first digit is a 0 and you add it with the remaining which is 3^n? But something seems missing. Please help!!! Also how should I set up my characteristic polynomial? (S(k))? I have S(k) = S(k-1) + k*3S(k-1) and trying to solve for the coefficients. But it doesn't seem to be quite right. Please help and thank you!
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 9T
Related questions
Question
Need help with this problem.
It states:
Determine the number of n-digit quaternary (0, 1, 2, 3) sequences (in closed form) where there is never a 3 anywhere to the right of a 0.
My current solution:
I split it up into two parts, one for if there is a 0 in the sequence and one without. I've gathered that there are 3^(n-1) possibilities if the first digit is a 0 and you add it with the remaining which is 3^n? But something seems missing. Please help!!!
Also how should I set up my characteristic polynomial? (S(k))?
I have S(k) = S(k-1) + k*3S(k-1) and trying to solve for the coefficients. But it doesn't seem to be quite right. Please help and thank you!
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning