A sequence of integers

A sequence $\{a_i\}_{i=1}^{\infty}$ of integers is defined by: $a_n= \begin{cases} 1 &\mbox{if } n \leq 3 \\ 0 & \mbox{if } n= 4 \\ \left ( a_{n-1} + a_{n-2} + a_{n-3} \right ) \pmod{2} & \mbox{if } n>4 \end{cases}$ Here $n \pmod{2}$ denotes the remainder when $n$ is divided by $2$ , i.e. $n \pmod{2}= \begin{cases} 0 & \mbox{if } n \equiv 0 \pmod{2} \\ 1 & \mbox{if } n \equiv 1 \pmod{2} \end{cases}$ Find the number of integers $n$ such that $1 \leq n <25$ and $a_n= 1$ .