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), 233-238
DOI: 10.12691/tjant-2-6-9
Open AccessArticle

Generalized Fibonacci – Like Sequence Associated with Fibonacci and Lucas Sequences

Yogesh Kumar Gupta1, , Mamta Singh2 and Omprakash Sikhwal3

1Schools of Studies in Mathematics, Vikram University Ujjain, (M. P.) India

2Department of Mathematical Sciences and Computer application, Bundelkhand University, Jhansi (U. P.)

3Department of Mathematics, Mandsaur Institute of Technology, Mandsaur (M. P.) India

Pub. Date: December 28, 2014

Cite this paper:
Yogesh Kumar Gupta, Mamta Singh and Omprakash Sikhwal. Generalized Fibonacci – Like Sequence Associated with Fibonacci and Lucas Sequences. Turkish Journal of Analysis and Number Theory. 2014; 2(6):233-238. doi: 10.12691/tjant-2-6-9

Abstract

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 Fn=Fn-1+Fn-2, , and F0=0, F1=1, where Fn is a nth number of sequence. Many authors have been defined Fibonacci pattern based sequences which are popularized and known as Fibonacci-Like sequences. In this paper, Generalized Fibonacci-Like sequence is introduced and defined by the recurrence relation Bn=Bn-1+Bn-2, with B0=2s, B1=s+1, where s being a fixed integers. Some identities of Generalized Fibonacci-Like sequence associated with Fibonacci and Lucas sequences are presented by Binet’s formula. Also some determinant identities are discussed.

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

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