Geodesic
On the rational recursive sequence $ x_{n+1}=\dfrac {\alpha_0x_n+\alpha_1x_{n-l}+\alpha _2x_{n-k}} {\beta_0x_n+\beta_1x_{n-l}+\beta_2x_{n-k}}$
Mathematica Bohemica, Tome 135 (2010) no. 3, pp. 319-336.

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The main objective of this paper is to study the boundedness character, the periodicity character, the convergence and the global stability of positive solutions of the difference equation $$ x_{n+1}=\frac {\alpha _0x_n+\alpha _1x_{n-l}+\alpha _2x_{n-k}} {\beta _0x_n+\beta _1x_{n-l}+\beta _2x_{n-k}}, \quad n=0,1,2,\dots $$ where the coefficients $\alpha _i,\beta _i\in (0,\infty )$ for $ i=0,1,2,$ and $l$, $k$ are positive integers. The initial conditions $ x_{-k}, \dots , x_{-l}, \dots , x_{-1}, x_0 $ are arbitrary positive real numbers such that $l$. Some numerical experiments are presented.
DOI : 10.21136/MB.2010.140707
Classification : 34C99, 39A10, 39A20, 39A22, 39A23, 39A30, 39A99, 65Q10
Keywords: difference equation; boundedness; period two solution; convergence; global stability 
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     title = {On the rational recursive sequence $ x_{n+1}=\dfrac {\alpha_0x_n+\alpha_1x_{n-l}+\alpha _2x_{n-k}} {\beta_0x_n+\beta_1x_{n-l}+\beta_2x_{n-k}}$},
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Zayed, E. M. E.; El-Moneam, M. A. On the rational recursive sequence $ x_{n+1}=\dfrac {\alpha_0x_n+\alpha_1x_{n-l}+\alpha _2x_{n-k}} {\beta_0x_n+\beta_1x_{n-l}+\beta_2x_{n-k}}$. Mathematica Bohemica, Tome 135 (2010) no. 3, pp. 319-336. doi : 10.21136/MB.2010.140707. http://geodesic.mathdoc.fr/articles/10.21136/MB.2010.140707/

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