# But, there's no information

Discrete Mathematics Level 4

Let $$a_{0}, a_{1}, a_{2}, \dots$$ be a sequence of positive real numbers such that $$a_{2014} = 2014$$, and $$a_{n} = 6a_{n-3}-4a_{n-1}-a_{n-2}$$ for all integers $$n \geq 3.$$ Find the sum of all possible values of $$a_{10000}.$$

×