Two generalizations of Lucas sequence

摘要

We define a generalization of Lucas sequence by the recurrence relation lm=blm-1+lm-2 (if m is even) or lm=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).