• GENERALIZED FIBONACCI-LUCAS SEQUENCE
Abstract
In this paper, we study Generalized Fibonacci-Lucas sequence {Hn} defined by the recurrence relation
Hn = Hn-1 + Hn-2, for all n ³ 2
H0 = 2 and H1 = m+1, m being a fixed positive integer. The associated initial conditions are the sum of initial conditions of Lucas sequence and m times the initial conditions of Fibonacci sequence respectively. We shall define Binet's formula and generating function of Generalized Fibonacci-Lucas sequence.
Mainly, Induction method and Binet's formula will be used to establish properties of Generalized Fibonacci-Lucas sequence.
Hn = Hn-1 + Hn-2, for all n ³ 2
H0 = 2 and H1 = m+1, m being a fixed positive integer. The associated initial conditions are the sum of initial conditions of Lucas sequence and m times the initial conditions of Fibonacci sequence respectively. We shall define Binet's formula and generating function of Generalized Fibonacci-Lucas sequence.
Mainly, Induction method and Binet's formula will be used to establish properties of Generalized Fibonacci-Lucas sequence.
Keywords
Fibonacci Sequence, Lucas Sequence, Generalized Fibonacci-Lucas Sequence.
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