Turkish Journal of Analysis and Number Theory
ISSN (Print): 2333-1100 ISSN (Online): 2333-1232 Website: http://www.sciepub.com/journal/tjant
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Turkish Journal of Analysis and Number Theory. 2014, 2(6), 193-197
DOI: 10.12691/tjant-2-6-1
Open AccessArticle

Generalized Fibonacci-Lucas Sequence

Bijendra Singh1, Omprakash Sikhwal2, 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

Pub. Date: November 23, 2014

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 Fn is a nth number of sequence. The Lucas Sequence is defined by the recurrence formula and L0=2, L1=1, where Ln is a nth 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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