# Solving an recursive sequence [closed]

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

The recursive sequence is:

$$f(0) = 4$$

$$f(1) = 14$$

$$f(2) = 194$$

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

## closed as off-topic by Steven Landsburg, user44191, RP_, David White, Piotr HajlaszMar 11 at 15:05

This question appears to be off-topic. The users who voted to close gave these specific reasons:

• "MathOverflow is for mathematicians to ask each other questions about their research. See Math.StackExchange to ask general questions in mathematics." – user44191, RP_, Piotr Hajlasz
• "This question does not appear to be about research level mathematics within the scope defined in the help center." – Steven Landsburg, David White
If this question can be reworded to fit the rules in the help center, please edit the question.

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