Two generalizations of Lucas sequence

Abstract

We define a generalization of Lucas sequence by the recurrence relation lm=blm-1+lm-2 (if m is even) or l m=alm-1+lm-2 (if m is odd) with initial conditions l0=2 and l1=a. We obtain some properties of the sequence {lm}m=0 and give some relations between this sequence and the generalized Fibonacci sequence {qm}m=0 which is defined in Edson and Yayenie (2009). Also, we give corresponding generalized Lucas sequence with the generalized Fibonacci sequence given in Yayenie (2011). © 2014 Elsevier Inc. All rights reserved.