6. Let a be the number of 1 x n tile designs you can make using 1 × 1 squares available in 4 colors and 1 x 2 dominoes available in 5 colors. a. First, find a recurrence relation to describe the problem. Explain why the recurrence relation is correct (in the context of the problem). b. Write out the first 6 terms of the sequence a1, a2,.... c. Solve the recurrence relation. That is, find a closed formula for an.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
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6. Let a be the number of 1 x n tile designs you can make using 1 × 1
squares available in 4 colors and 1 x 2 dominoes available in 5 colors.
a. First, find a recurrence relation to describe the problem. Explain why the
recurrence relation is correct (in the context of the problem).
b. Write out the first 6 terms of the sequence a1, a2,....
c. Solve the recurrence relation. That is, find a closed formula for an.
Transcribed Image Text:6. Let a be the number of 1 x n tile designs you can make using 1 × 1 squares available in 4 colors and 1 x 2 dominoes available in 5 colors. a. First, find a recurrence relation to describe the problem. Explain why the recurrence relation is correct (in the context of the problem). b. Write out the first 6 terms of the sequence a1, a2,.... c. Solve the recurrence relation. That is, find a closed formula for an.
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