Abstract
In this paper, some cases on the periodicity of the rational difference equation
Sn+1 = Sn-p(aS(n-p) + bS(n-r) + cS(n-s)/dS(n-q) + eS(n-r) + fS(n-s)),
are investigated, where a, b, c, d, e, f is an element of (0, infinity). The initial conditions S-p, S-p+1,...,S-q, S-q+1,...,S-r,..., S-r+1,...,S-s,...,S-s+1,...,S-1 and S-0 are arbitrary positive real numbers such that p > q > r > s >= 0. Some numerical examples are provided to illustrate the theoretical discussion.