Let $x\_1, x\_2,\ldots$ be real numbers so that for all $n > 0,$
$$x\_{n+3} = x\_{n+2} - 2x\_{n+1} + x\_n. $$
Suppose $x\_1 = x\_3 = 1$ and you're given that $x\_{98} = x\_{99}$.

Find the sum $x\_1 + x\_2 + \ldots + x\_{100}$.