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 Hajlasz Mar 11 at 15:05

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

  • $\begingroup$ sorry i forgot to say that --> f(0) = 4 $\endgroup$ – raimannma Mar 11 at 13:28
  • $\begingroup$ perfect thank you very much $\endgroup$ – raimannma Mar 11 at 13:57

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