On the recursive sequence xn+1 = xn-7/1+xn-3

Abstract

In this paper the solutions of the following difference equation is examined: x n+1 = x n−7 1 + x n−3

Note on a difference equation and some of its relatives

“…Here we show that this is not the case. Namely, we show that all the results in previous studies, 20,21 as well as in the papers which studied the Equations () and (), easily follow from some ones in Stević 22…”

“…Bearing in mind that paper, 20 which deals with Equation (), works only on some problems described in Theorem 1, its results directly follow from the statements in the theorem. Namely, the paper, as well as Simsek and Ogul 21 and those dealing with Equations () and (), dealt only with the problems in the statements (a) ‐ (f) in Theorem 1, following the details of the proofs of the statements given in Stević, 22 and making some technical changes.…”

“…Many results on difference equations and systems have appeared in the last two to three decades, because of their numerous applications in various branches of science. For some of them see, for example, previous studies, 1–33 as well as the cited papers therein.…”

“…In Simsek et al, 20 it has been recently studied the following equation where it is also quoted the following equation as well as …”

“…The following generalization of Equations ()–() has been also previously studied in the literature (see 21 ), but this fact was not mentioned in 20 …”