DK-GEORGMOHR 2007 Problem 5

The sequence of numbers $a_0,a_1,a_2,...$ is determined by $a_0 = 0$ , and $$a_n= \begin{cases} 1+a_{n-1} \,\, when\,\, n \,\, is \,\, positive \,\, and \,\, odd 3a_{n/2} \,\, when \,\, n \,\, is \,\, positive \,\, and \,\, even\end{cases}$$ How many of these numbers are less than $2007$ ?