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On the difference equation \(x_{n+1}=x_nx_{n-2}-1\). (English) Zbl 1216.39016

Summary: The long-term behavior of solutions of the following difference equation: \(x_{n+1}=x_nx_{n-2}-1\), \(n\in\mathbb N_0\), where the initial values \(x_{-2}, x_{-1}, x_0\) are real numbers, is investigated.

MSC:

39A22 Growth, boundedness, comparison of solutions to difference equations
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