# A sequence of integers

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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 $$a_n= 1$$.

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