$U_{n+1} = 2U_n^2 - 1$ I need to find the general term for the progression defined by :
$U_{n+1} = 2U_n^2 - 1$
Can any one help me out ? Is it even possible to find the general term ?

HINT: Notice that 
$$2x^2-1=\cos(2\arccos(x))$$
for $x\in [-1,1]$, and
$$2x^2-1=\cosh(2\operatorname{arccosh}(x))$$
for $x\notin [-1,1]$.
Also observe that if $s(x)=2x^2-1$, then
$$U_{n+1}=s(U_n)$$
