Turkish Journal of Analysis and Number Theory
ISSN (Print): 2333-1100 ISSN (Online): 2333-1232 Website: http://www.sciepub.com/journal/tjant
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Turkish Journal of Analysis and Number Theory. 2014, 2(5), 170-175
DOI: 10.12691/tjant-2-5-3
Open AccessArticle

Identities of Generalized Fibonacci-Like Sequence

Mamta Singh1, Omprakash Sikhwal2 and Yogesh Kumar Gupta3,

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

Pub. Date: October 08, 2014

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 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.

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

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