Integer sequences that behave as Fibonacci-Lucas pairs

Abstract

There have been a number of articles on the relation between the terms of the Fibonacci and Lucas sequences and how they are closely related to trigonometric and hyperbolic functions and their properties [1]. This article is based on other integer sequences. It sets out to determine other pairs of such sequences that have the same relation as the Fibonacci and Lucas have to each other. So we shall be concerned with second order recurrence relations with constant coefficients:and pairs of sequences (un) and (vn) that each satisfy it. We seek a condition that ensures the pair of sequences behave as the Fibonacci-Lucas pair behave.