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. Top Keywords k-Pell sequence, k-Pell-Lucas sequence, Recurrence relation. Top |