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Research Journal of Science and Technology
Year : 2017, Volume : 9, Issue : 4
First page : ( 656) Last page : ( 662)
Print ISSN : 0975-4393. Online ISSN : 2349–2988.
Article DOI : 10.5958/2349–2988.2017.00112.7

On the Properties of Generalized k-Pell like Sequence

 Pankaj*

Department of Mathematics, Indira Gandhi University, Meerpur (Rewari)-122502, Haryana, India

*Corresponding Author E-mail: pankajarora1242@yahoo.com

Online published on 12 June, 2018.

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 {Mk,n}n=1, with initial conditions Mk,o = 2,Mk,1 = m + 2, which is generated by the recurrence relation Mk,n+1 = 2Mk,n + kMk,n-1 for n ╥ 1, where k,m are integer numbers. We produce an extended Binet's formula for Mk,n and thereby the identities such as Catalan's, Simpson's, d’ Ocagene's etc.

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Keywords

k-Pell sequence, k-Pell-Lucas sequence, Recurrence relation.

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