 # Suppose we can only use 5 kinds of tiles to cover a 1 times n board: (1) 1 times 1 size with red color, (2) 1 times 1 size with blue color, (3) 1 times 2 size with black color, (4) 1 times 2 size with green color, (5) 1 times 2 size with white color. Let W(n) be the number of ways to tile the 1 times n board, n=1,2,…. Alex Baird 2022-07-18 Answered
Suppose we can only use 5 kinds of tiles to cover a $1×n$ board:
(1) $1×1$ size with red color,
(2) $1×1$ size with blue color,
(3) $1×2$ size with black color,
(4) $1×2$ size with green color,
(5) $1×2$ size with white color.
Let W(n) be the number of ways to tile the $1×n$ board, $n=1,2,\dots$
For example, $W\left(1\right)=2$, $W\left(2\right)=7$.
What is the W(n) equation?
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Step 1
$W\left(n+1\right)=2×W\left(n\right)+3×W\left(n-1\right)$
Step 2
When $W\left(0\right)=1$