On the Properties of Generalized k-Pell like Sequence
Department of Mathematics, Indira Gandhi University, Meerpur (Rewari)-122502, Haryana, India
*Corresponding Author E-mail:pankajarora1242@yahoo.com
ABSTRACT:
The Pell sequence has been generalized in many ways, some by preserving the initial conditions, others by preserving the recurrence relation. In this paper, we define a new generalization with initial conditions which is generated by the recurrence relation for where are integer numbers. We produce an extended Binet’s formula for and thereby the identities such as Catalan’s, Simpson’s, d’ Ocagene’s etc.
KEYWORDS: k-Pell sequence, k- Pell-Lucas sequence, Recurrence relation.
2010 Mathematics Subject Classification:11Bxx, 11B39, 11B83
1. INTRODUCTION
The well known Pell and Pell-Lucas sequences have many interesting properties [1-6]. They are defined for with recurrences and receptively. In the literature, these numbers have been generalized in many ways [7-13]. In this paper, we define generalized k-Pell like sequence and give some special identities of this generalization.This paper contributes to k-Pell numbers literature, and encourages many researchers to investigate the properties of such number sequences.
2. THE GENERALIZED k-PELL LIKE SEQUENCE
3. FUNDAMENTAL PROPERTIES OF GENERALIZED k-PELL LIKE SEQUENCE
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Received on 10.08.2017 Modified on 26.08.2017
Accepted on 21.09.2017 ©A&V Publications All right reserved
Research J. Science and Tech. 2017; 9(4):656-662.
DOI: 10.5958/2349-2988.2017.00112.7