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I entered the following recurrence relation into RSolve and it just gave the question back to me. $$a_{n+1} = \frac{(1+a_n +(a_{n−1})^3)} 3$$

Is there another way to get a formula for the nth term?

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indeed RSolve[{a[n + 1] == (1 + a[n] + a[n - 1]^3 )/3, a[1] == 0, a[2] == 0}, a[n], n] –  chris Apr 14 '13 at 6:44
It is generally difficult to obtain explicit solutions for nonlinear recurrences. Do you have any reason why you're supposed to expect a closed form solution? –  J. M. Apr 14 '13 at 6:51
There is an undocumented function, SequenceLimit[], which you might be interested in, if what you want is to numerically estimate the limit of your sequence. –  J. M. Apr 14 '13 at 7:09
Well you can always turn it into a system of first order difference equations and get the equilibrium points and their stable and unstable manifolds around them. This will give you a better picture of the dynamics of the equation. –  Spawn1701D Apr 14 '13 at 7:18
@Spawn1701D. Thanks for the tip. That sounds promising. Can you tell me where to find an explanation of such methods. –  jim Apr 14 '13 at 12:37

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