Supposing that $m$ is an integer and that$$a_{n+1}={a_n}^2+m \ \ (n=1, 2,\cdots),$$ represent $a_n$ by $a_1$ and $n$.
I'm interested in this question because I got the following.
If $m=-2$, then $$a_n={{\left({\frac{a_1+\sqrt{{a_1}^2-4}}{2}}\right)}^{2^{n-1}}+{\left({\frac{a_1-\sqrt{{a_1}^2-4}}{2}}\right)}^{2^{n-1}}}.$$
However, I don't have any good idea for $m\neq-2$. I need your help.
