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On the solutions of two special types of Riccati difference equation via Fibonacci numbers. (English) Zbl 1390.39020
Summary: In this study, we investigate the solutions of two special types of the Riccati difference equation $$x_{n+1}=\frac{1}{1+x_n}$$ and $$y_{n+1}=\frac{1}{-1+y_n}$$ such that their solutions are associated with Fibonacci numbers.

##### MSC:
 39A10 Additive difference equations 39A13 Difference equations, scaling ($$q$$-differences) 11B39 Fibonacci and Lucas numbers and polynomials and generalizations
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