MathNet 2019-part-05 — 184 problems (EN–VI) Question 106

The sequence $(x_n)_{n \ge 1}$ fulfils $x_{n+3} = x_n + x_{n+1} + x_{n+2}$, for every $n \in \mathbb{N}^*$. Find $x_1, x_2, x_3 \in \mathbb{Q} \cap (0, 1)$, so that $(x_n)_{n \ge 1}$ has a limit.