# General term of sequence $a_0=2$ and $a_{n+1}=2a_n^2-1$

Is it possible to find general term of this sequence? $a_0=2$ and $a_{n+1}=2a_n^2-1$

set $\alpha = \cosh^{-1}(2)$ then : $a_n=\cosh(2^n \alpha)$.
It is easy to prove it by induction using $\cosh(2x)=2\cosh^2(x)-1$.
Why $\cosh$ and not $\cos$ ? because $a_0>1$, if $a_0=0.5$ for example I'll use $\cos$.