MathNet 2020 — Math Olympiad Vault — Part 04 Question 147

Let $a_0=1$, $a_1=(1+\sqrt3)/(2\sqrt2)$ and $a_n=2a_1a_{n-1}-a_{n-2}$ for $n\ge2$. Find $a_{2020}$ and $\lim_{n\to\infty}a_n/n^2$.