How many ways?

Let $k(n)$ difine the number of ways a $2\times n$ rectangle can be tiled with rectangular tiles of size $2\times1$ is.

From the figure above it is easy to see that $k(x)+k(x+1)=k(x+2)$ . Since $k(1)=1, k(2)=2$ , by calculating we get $k(8)=34$ .

Note: $k(m)$ is the $m+1.$ item of the Fibonacci sequence .