## Article citationsMore >>

A. F. Horadam: A Generalized Fibonacci Sequence, American Mathematical Monthly, Vol. 68. (5), 1961, 455-459.

**has been cited by the following article:**

## Article

# Generalized Fibonacci-Lucas Sequence

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

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

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

*Turkish Journal of Analysis and Number Theory*.

**2014**, Vol. 2 No. 6, 193-197

**DOI:**10.12691/tjant-2-6-1

**Copyright © 2014 Science and Education Publishing**

**Cite this paper:**

Bijendra Singh, Omprakash Sikhwal, 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.

Correspondence to: Omprakash Sikhwal, Department of Mathematics, Mandsaur Institute of Technology, Mandsaur (M. P.), India. Email: opbhsikhwal@rediffmail.com

## 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 F

_{0}=0, F_{1}=1, where F_{n}is a n^{th }number of sequence. The Lucas Sequence is defined by the recurrence formula and L_{0}=2, L_{1}=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 B_{0}= 2b, B_{1}= 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.