# Simple sequence made complicated

Discrete Mathematics Level 3

A sequence $$a_{n}$$ satisfies the following equation:

$$a_{n} = 4a_{n-1} - 5a_{n-2} + 2a_{n-3}$$, for all positive integers $$n$$ not less than $$3$$

If $$a_{0} = 1, a_{1} = 2, a_{2} = 3,$$

Find $$a_{1000}$$

This question will be lengthy if you substitute for $$a_{3}, a_{4}, a_{5}, ...$$ directly. Try to find the general form of $$a_{n}$$

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