A generalization of Lucas sequence and associated identities

Abstract

In this paper, we attempt to generalize Lucas sequence by generating certain number of sequences whose terms are obtained by adding the last two generated terms of the preceding sequence. Lucas sequence is obtained as a particular case of generating only one sequence. Moreover we prove some of the results which can be seen as generalized form of the results which hold for Lucas sequence. We obtain Cassini-like identity for these generalized Lucas sequences.