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For linear recurrence, we can use generating function. So is there a general technique to solve non-linear recurrence or it depends on a specific sequence? For example, $a_{n+1} = \dfrac{a_n(a_n - 3)}{4}$ for $a_0 = a$

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    Thank you all! Sequences are actually more mysterious than I initially thought.2012-11-04

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As already mentioned, currently for non-linear recurrence relations, there are no known general techniques for obtaining a closed form solution.

For the very few non-linear recurrences that are actually solvable, the techniques used to solve them are strongly dependent on the specific recurrence that your dealing with.