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

The recursive sequence is:

$f(0) = 4$

$f(1) = 14$

$f(2) = 194$

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

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

The recursive sequence is:

$f(0) = 4$

$f(1) = 14$

$f(2) = 194$

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

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