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arXiv · 1902.06520

On certain rational recursive sequences of order four

Mensah Folly-Gbetoula·Darlison Nyirenda
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Abstract

We obtain solutions to the recursive sequences of the form $$x_{n + 1} = \frac{x_{n - 3}x_{n }}{x_{n - 2}(a_n + b_nx_{n -3}x_{n})}$$ where $a_n$ and $b_n$ are arbitrary sequences of real numbers, and the initial values are gives as; $x_{-3},x_{-2}, x_{-1}$ and $x_{0}$. Our methodology is to employ a group theoretic method which lowers the order of the equations, and then solve the resulting lower order recurrence relations that arise therefrom.

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Mensah Folly-Gbetoula, Darlison Nyirenda. 2019-02-18. On certain rational recursive sequences of order four. https://arxiv.org/abs/1902.06520

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