Generalized Fibonacci-Lucas Sequence

Bijendra Singh¹, Omprakash Sikhwal^2, and Yogesh Kumar Gupta³

¹School of Studies in Mathematics, Vikram University, Ujjain-456010 (M. P.), India

²Department of Mathematics, Mandsaur Institute of Technology, Mandsaur (M. P.), India

³School of Studies in Mathematics, Vikram University, Ujjain, (M. P.), India

Cite this paper:
Bijendra Singh, Omprakash Sikhwal and Yogesh Kumar Gupta. Generalized Fibonacci-Lucas Sequence. Turkish Journal of Analysis and Number Theory. 2014; 2(6):193-197. doi: 10.12691/tjant-2-6-1

Abstract

The Fibonacci sequence is a source of many nice and interesting identities. A similar interpretation exists for Lucas sequence. The Fibonacci sequence, Lucas numbers and their generalization have many interesting properties and applications to almost every field. Fibonacci sequence is defined by the recurrence formula and F₀=0, F₁=1, where F_n is a n^th number of sequence. The Lucas Sequence is defined by the recurrence formula and L₀=2, L₁=1, where L_n is a n^th number of sequence. In this paper, Generalized Fibonacci-Lucas sequence is introduced and defined by the recurrence relation with B₀ = 2b, B₁ = s, where b and s are integers. We present some standard identities and determinant identities of generalized Fibonacci-Lucas sequences by Binet’s formula and other simple methods.

Keywords:
Fibonacci sequence Lucas sequence Generalized Fibonacci-Lucas sequence Binet’s formula

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