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
Turkish Journal of Analysis and Number Theory.
2014,
Vol. 2 No. 6, 233-238
DOI: 10.12691/tjant-2-6-9
Copyright © 2014 Science and Education PublishingCite this paper: Yogesh Kumar Gupta, Mamta Singh, 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.
Correspondence to: Yogesh Kumar Gupta, Schools of Studies in Mathematics, Vikram University Ujjain, (M. P.) India. Email:
yogeshgupta.880@rediffmail.comAbstract
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 F
0=0, F
1=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 B
0=2s, B
1=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