How to solve quadratic recurrence relation How to solve recurrence relation of the following form:

$U_n = a \times U_{n-1}^2 + b \times U_{n-1} + c$

where: $-1 &lt; a &lt; 0$ , $b = 1 - a$ , $c &gt; 0$

Edit

I found here more cases where a quadratic recurrence is solvable.
Hint:

According to https://en.wikipedia.org/wiki/Iterated_function#Examples,

$U_n$ has easier forms when $c=\dfrac{(1-a)^2-2(1-a)}{4a}$ and $c=\dfrac{(1-a)^2-2(1-a)-8}{4a}$ .
With a few exceptions, general solutions of quadratic (or higher) recurrences can't be expressed in closed form.  This one is not an exception.