2005 AIME II Problem 11

Let m be a positive integer, and let a_{0}, a_{1}, \ldots, a_{m} be a sequence of real numbers such that a_{0}=37, a_{1}=72, a_{m}=0, and

$$a_{k+1}=a_{k-1}-\frac{3}{a_{k}}$$

for k=1,2, \ldots, m-1. Find m.