How do i compute $f_n = 3f_{n-1} + 2\sqrt{2f_{n-1}^2 – 2}$ for n around 10^18?

So I have the reccurence $ $ f_n = \begin{cases} 3f_{n-1} + 2\sqrt{2f_{n-1}^2 – 2}, &n > 0\ 3, &n > 1\ \end{cases}$ $ and I need to compute it in $ \lg(n)$ , for n as big as $ 10^{18}$ . I tried to reduce it to a closed form equation but I don’t see how that could be achieved.