Staircase climbs using jumps of two or more

A rabbit stands at the bottom of a $10$-step staircase. Every hop moves it up by at least $2$ steps (any number of steps that is $2$ or more). How many different sequences of hops take it exactly to the top of step $10$?

$34$. Count compositions of 10 into parts of size at least 2. If $h_n$ is the count for $n$ steps, removing the last stair from a final hop of size at least 3, or deleting a final hop of size exactly 2, gives $h_n=h_{n-1}+h_{n-2}$ with $h_0=1,h_1=0$. That is a Fibonacci sequence and $h_{10}=34$.