Example 4.2.10 Using $1 \times 2$ dominoes to cover a $2 \times n$ grid, how many covering schemes are there.
Solution: Let $F_{n}$ be the number of covering schemes. Since there are only two ways to cover a small square in one row and one column (Figure 4-29), the first covering method has a total of $F_{n-1}$ ways, and the second covering method has a total of $F_{n-2}$ ways, hence $F_{n}=F_{n-1}+F_{n-2}$.
It is also easy to see that $F_{1}=1, F_{2}=2$, so $F_{n}$ is a Fibonacci number.