Try Finding The First Few Terms!

$\large a_{i}= 2a_{i-1} −a_{i-2} +2$

Define the sequence $${(a_{n}})$$ with intial terms $$a_{0} = 0, a_{1} = 1$$, satisfying the recurrence relations above for all $$i \geq 2.$$ Determine the value of $$a_{1000}$$.

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