I have an recursive sequence and want to convert it to an explicit formula.


The recursive sequence is:


$f(0) = 4$


$f(1) = 14$


$f(2) = 194$


$f(x+1) = f(x)^2 - 2$



Solving an recursive sequence
$$f(x+1) = f(x)^2 - 2,\;\;f(0)=4$$
$$\Rightarrow f(x)=2\cos\left(2^x\arccos 2\right)=2 \cosh \left(2^x \ln \left(\sqrt{3}+2\right)\right)$$


