International Journal of Mathematics and Mathematical Sciences
Volume 27 (2001), Issue 1, Pages 1-6
doi:10.1155/S0161171201010614

On the recursive sequence xn+1=−1/xn+A/xn−1

Abstract

We investigate the periodic character of solutions of the nonlinear difference equation xn+1=−1/xn+A/xn−1. We give sufficient conditions under which every positive solution of this equation converges to a period two solution. This confirms a conjecture in the work of DeVault et al. (2000).