Generalized Fibonacci – Like Sequence Associated with Fibonacci and Lucas Sequences

Yogesh Kumar Gupta^1, , 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

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 F_n=F_n-1+F_n-2, , and F₀=0, F₁=1, where F_n is a n^th 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 B_n=B_n-1+B_n-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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