# Linear Recurrence With Little Information

Probability Level 4

An infinite sequence of real numbers $a_1,a_2,\ldots$ satisfies the recurrence $a_{n+3}=a_{n+2}-2a_{n+1}+a_n$ for every positive integer $n$.

Given that $a_1=a_3=1$ and $a_{98}=a_{99}$, compute $a_1+a_2+\cdots+a_{100}$.

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