On fourteen solvable systems of difference equations

In this paper, we mainly consider the systems of difference equationsxn+1=1+pnqn,yn+1=1+rnsn,n∈N0,where each of the sequences pn,qn,rn and sn represents either the sequence xn or the sequence yn, with nonzero real initial values x0 and y0. Then we solve fourteen out of sixteen possible systems. It i...

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Bibliographic Details
Published inApplied mathematics and computation Vol. 233; pp. 310 - 319
Main Authors Tollu, D.T., Yazlik, Y., Taskara, N.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.05.2014
Subjects
Fibonacci numbers
General solution
Riccati difference equation
System of difference equations
System of difference equations
Riccati difference equation
General solution
Fibonacci numbers
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Summary:In this paper, we mainly consider the systems of difference equationsxn+1=1+pnqn,yn+1=1+rnsn,n∈N0,where each of the sequences pn,qn,rn and sn represents either the sequence xn or the sequence yn, with nonzero real initial values x0 and y0. Then we solve fourteen out of sixteen possible systems. It is noteworthy to depict that the solutions are presented in terms of Fibonacci numbers for twelve systems of these fourteen systems.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2014.02.001