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# Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia

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Volume 68, Issue 3

# On the solutions of a second-order difference equation in terms of generalized Padovan sequences

Yacine Halim
/ Julius Fergy T. Rabago
• Department of Mathematics and Computer Sciences College of Science, University of the Philippines, Gov. Pack Road, Baguio City, 2600, Benguet, Philippines
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Published Online: 2018-05-18 | DOI: https://doi.org/10.1515/ms-2017-0130

## Abstract

This paper deals with the solution, stability character and asymptotic behavior of the rational difference equation

$xn+1=αxn−1+βγxnxn−1,n∈N0,$

where ℕ0 = ℕ ∪ {0}, α, β, γ ∈ ℝ+, and the initial conditions x–1 and x0 are non zero real numbers such that their solutions are associated to generalized Padovan numbers. Also, we investigate the two-dimensional case of the this equation given by

$xn+1=αxn−1+βγynxn−1,yn+1=αyn−1+βγxnyn−1,n∈N0.$

MSC 2010: Primary 39A10; Secondary 40A05

This work was supported by LMAM Laboratory, Jijel University.

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Accepted: 2017-11-05

Published Online: 2018-05-18

Published in Print: 2018-06-26

Citation Information: Mathematica Slovaca, Volume 68, Issue 3, Pages 625–638, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918,

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