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
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 PublishingCite 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.comAbstract
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.
Keywords