Let an be the number of 1 x n tile designs you can make using 1 x 1 squares available in 5 colors and 1 x 2 dominoes available in 6 colors. a. First, find a recurrence relation to describe the problem. An b. Write out the first 6 terms of the sequence a1, a2, ... = In A2 a3 a5 %3D a6 = c. Solve the recurrence relation. That is, find a closed formula. An
Let an be the number of 1 x n tile designs you can make using 1 x 1 squares available in 5 colors and 1 x 2 dominoes available in 6 colors. a. First, find a recurrence relation to describe the problem. An b. Write out the first 6 terms of the sequence a1, a2, ... = In A2 a3 a5 %3D a6 = c. Solve the recurrence relation. That is, find a closed formula. An
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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I found the first couple terms but unable to find the rest. I want to see where I ran my mistake.
![Let \( a_n \) be the number of \( 1 \times n \) tile designs you can make using \( 1 \times 1 \) squares available in 5 colors and \( 1 \times 2 \) dominoes available in 6 colors.
a. First, find a recurrence relation to describe the problem.
\[
a_n =
\]
b. Write out the first 6 terms of the sequence \( a_1, a_2, \ldots \)
\[
\begin{align*}
a_1 &= \\
a_2 &= \\
a_3 &= \\
a_4 &= \\
a_5 &= \\
a_6 &=
\end{align*}
\]
c. Solve the recurrence relation. That is, find a closed formula.
\[
a_n =
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Transcribed Image Text:Let \( a_n \) be the number of \( 1 \times n \) tile designs you can make using \( 1 \times 1 \) squares available in 5 colors and \( 1 \times 2 \) dominoes available in 6 colors.
a. First, find a recurrence relation to describe the problem.
\[
a_n =
\]
b. Write out the first 6 terms of the sequence \( a_1, a_2, \ldots \)
\[
\begin{align*}
a_1 &= \\
a_2 &= \\
a_3 &= \\
a_4 &= \\
a_5 &= \\
a_6 &=
\end{align*}
\]
c. Solve the recurrence relation. That is, find a closed formula.
\[
a_n =
\]
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