# Recurring Styles #9 - Integers for a Condition!

$\large{(n+1)(n-2)x_{n+1} = n(n^2 - n - 1)x_n - (n-1)^3 x_{n-1}}$

Let $$(x_n)_{n \geq 2}$$ be a sequence such that $$x_2 = 1, x_3 = 1$$, and for all $$n \geq 3$$, the above recurrence relation satisfies.

For which all values of $$n, \ n \geq 4$$ is every $$x_n$$ an integer?

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