HMMT 2004 U14

If $a_{1}=1, a_{2}=0$ , and $a_{n+1}=a_{n}+\frac{a_{n+2}}{2}$ for all $n \geq 1$ , compute $a_{2004}$ .

Dataset text NuminaMath olympiads. Quoted with source.

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-2^{1002}

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