Identities of Generalized Fibonacci-Like Sequence

Mamta Singh¹, Omprakash Sikhwal² and Yogesh Kumar Gupta^3,

¹Department of Mathematical Sciences and Computer application, Bhundelkhand University, Jhansi (U. P.) India

²Department of Mathematics, Mandsaur Institute of Technology, Mandsaur (M. P.) India

³Schools of Studies in Mathematics, Vikram University Ujjain, (M. P.) India

Cite this paper:
Mamta Singh, Omprakash Sikhwal and Yogesh Kumar Gupta. Identities of Generalized Fibonacci-Like Sequence. Turkish Journal of Analysis and Number Theory. 2014; 2(5):170-175. doi: 10.12691/tjant-2-5-3

Abstract

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

Keywords:
Fibonacci sequence Lucas Sequence Generalized Fibonacci-Like Sequence Binet’s Formula

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