Given the sequence $a_1 = 1$ and $a_2 = 1 $ with: $ a_n = 1 - \frac{a_{n-1} a_{n-2}}{4} $
Does there exist a closed form computing $a_n$ ? At the moment I have a problem getting a grip on the series: I think it is neither monotone increasing nor monotone decreasing but rather fluctuating around some values (it is bounded and thus must have a least one converging subsequence)
As always: I am happy about any constructive hint, comment or answer to the problem.