Science and Education Publishing
Turkish Journal of Analysis and Number Theory
2
5
2014
10
08
Identities of Generalized Fibonacci-Like Sequence
170
175
EN
Mamta
Singh
Omprakash
Sikhwal
Yogesh Kumar
Gupta
Schools of Studies in Mathematics, Vikram University Ujjain, (M. P.) India
TJANT2014253
10.12691/tjant-2-5-3
2014
08
16
2014
09
16
2014
10
08
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.