# Linear Recurrence With Little Information

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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