Ways to climb ten stairs in hops of one or two

A rabbit starts on the floor below a $10$-step staircase. Each hop takes it up either one step or two steps. In how many different hop sequences can it end exactly on the top (10th) step?

$89$. If $x_n$ counts the ways to reach step $n$, the final hop is from step $n-1$ or $n-2$, so $x_n=x_{n-1}+x_{n-2}$ with $x_1=1$, $x_2=2$. This is the Fibonacci sequence shifted by one, and $x_{10}=F_{11}=89$.