Setting the 'recursive relation' becomes...
... which is linear...
the problem is following quadratic recurrence equation:
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.