Title: Generalized Fibonacci-Like Sequence and its Properties
Abstract: The Fibonacci Sequence can be generalized in several ways. Similar is the case with Lucas Sequence. In this paper, we study Generalized Fibonacci-Like sequence {M n} defined by the recurrence relation Mn = M n-1 + M n-2, for all n ≥ 2 with M0 = 2m and M 1 = 1+m, m being a fixed positive integer. The associated initial conditions are the sum of initial conditions of Fibonacci sequence and m times the initial conditions of Lucas sequence respectively. We shall define Binet's formula and generating function of Generalized Fibonacci-Like sequence. Mainly, Induction method and Binet's formula will be used to establish properties of Generalized Fibonacci-Like sequence.
Publication Year: 2012
Publication Date: 2012-01-01
Language: en
Type: article
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Cited By Count: 5
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