Hello,

the problem is following quadratic recurrence equation:

$\displaystyle u_0=1$

$\displaystyle u_1=2$

$\displaystyle u_n=u_{n-2}^2u_{n-1}, \ n \geq 2$

I know how to solve most of the linear homogeneous and non-homogeneous equations, but I haven't encountered quadratic equations before. I tried googling and using forums search function, but I couldn't found any information, how to solve these. So, any help is appreciated. Thanks!

WolframAlpha gives following solution, but that doesn't help me either.