eng
Science and Education Publishing
Turkish Journal of Analysis and Number Theory
2014-10-08
2
5
170
175
10.12691/tjant-2-5-3
TJANT2014253
article
Identities of Generalized Fibonacci-Like Sequence
Mamta Singh
1
Omprakash Sikhwal
2
Yogesh Kumar Gupta
yogeshgupta.880@rediffmail.com
3
Department of Mathematical Sciences and Computer application, Bhundelkhand University, Jhansi (U. P.) India
Department of Mathematics, Mandsaur Institute of Technology, Mandsaur (M. P.) India
Schools of Studies in Mathematics, Vikram University Ujjain, (M. P.) India
The Fibonacci and Lucas sequences are well-known examples of second order recurrence sequences. 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, n≥2 and F0=0, F1=1, where Fn is a nth number of sequence. Many authors have 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 Mn=Mn-1+Mn-2, n≥2, with M0=2, M1=s+1, where s being a fixed integers. Some identities of Generalized Fibonacci-Like sequence are presented by Binet's formula. Also some determinant identities are discussed.
http://pubs.sciepub.com/tjant/2/5/3/tjant-2-5-3.pdf
Fibonacci sequence
Lucas Sequence
Generalized Fibonacci-Like Sequence
Binet's Formula