This can be solved computationally, but is there an analytical solution? I've tried to build a solution and it wasn't pretty. $$x_{n+1} = 3{(x_n)}^2+2 \qquad x_0 = 2$$
Can the recursion $x_{n+1} = 3{(x_n)}^2+2$ with $x_0 = 2$, be solved?
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recurrence-relations
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2The recursion $$z\mapsto z^2+c$$ is well known to have no analytical solution in general (some entire books with nice images have been written on the subject). – 2017-02-05