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Mock AIME 3 Pre 2005 Problems/Problem 10

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$10.$ $\{A_n\}_{n \ge 1}$ is a sequence of positive integers such that

$a_{n} = 2a_{n-1} + n^2$

for all integers $n > 1$. Compute the remainder obtained when $a_{2004}$ is divided by $1000$ if $a_1 = 1$.

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