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, $n = 1, 2, \ldots$.
For example, $W(1) = 2$, $W(2) = 7$, as shown by the following figure.
What is the $W(n)$ equation?