Climbing ten steps using only odd-sized jumps

A rabbit at the bottom of a $10$-step staircase climbs to the top using jumps that each cover an odd number of steps ($1$, $3$, $5$, …). How many different jump sequences take it exactly to the top of the tenth step?

$55$. Let $o_n$ count ways to climb $n$ steps. Splitting on whether the first jump is $1$ or larger (a jump of $j\ge3$ is like a jump of $j-2$ from two steps higher) gives $o_n=o_{n-1}+o_{n-2}$ with $o_1=o_2=1$, so $o_n$ is Fibonacci and $o_{10}=55$.