# Magic Sequences

A magic sequence is a sequence of non-negative integers $$x_0$$ to $$x_{n-1}$$ such that there are exactly $$x_i$$ instances of $$i$$, for all $$i$$.

$$\left( 2, 0, 2, 0 \right )$$ is a magic sequence of length $$4$$ since there are 2 0's, 0 1’s, 2 2’s and 0 3’s.

How many magic sequences of length 2015 exist?

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