# Divisibility of a recursive sequence.

Let $$a_{1}=1$$ and $$a_{2}=3$$ and for $$n > 2$$ $a_{n}=(n+1)a_{n-1} - na_{n-2}$ For how many positive integers $$n \leq 1000$$ is $$a_{n}$$ divisible by $$11$$?

Details and Assumptions

Computation devices are not necessary.

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