RU-ALLRUSSIAN 1962 Problem 3

Given integers $\mathrm{a_0}$ , $\mathrm{a_1}$ , ..., $\mathrm{a_{100}}$ , satisfying $\mathrm{a_1 > a_0}$ , $\mathrm{a_1 > 0}$ , and $\mathrm{a_{r + 2} = 3}$ $\mathrm{a_{r + 1}} - 2\mathrm{a_r}$ for $\mathrm{r} = 0$ , 1, ..., 98. Prove $\mathrm{a_{100} > 2^{99}}$ .