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On The Properties of Generalized k-Pell Like Sequence


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

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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 {π‘€π‘˜,𝑛}𝑛=1∞, with initial conditions π‘€π‘˜,0=2,π‘€π‘˜,1=π‘š+2, which is generated by the recurrence relation π‘€π‘˜,𝑛+1=2π‘€π‘˜,𝑛+π‘˜π‘€π‘˜,π‘›βˆ’1, for 𝑛β‰₯1, where π‘˜,π‘š are integer numbers. We produce an extended Binet’s formula for π‘€π‘˜,𝑛 and thereby the identities such as Catalan’s, Simpson’s, d’ Ocagene’s etc.

Keywords

k-Pell Sequence, k- Pell-Lucas Sequence, Recurrence Relation.
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  • On The Properties of Generalized k-Pell Like Sequence

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Authors

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

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 {π‘€π‘˜,𝑛}𝑛=1∞, with initial conditions π‘€π‘˜,0=2,π‘€π‘˜,1=π‘š+2, which is generated by the recurrence relation π‘€π‘˜,𝑛+1=2π‘€π‘˜,𝑛+π‘˜π‘€π‘˜,π‘›βˆ’1, for 𝑛β‰₯1, where π‘˜,π‘š are integer numbers. We produce an extended Binet’s formula for π‘€π‘˜,𝑛 and thereby the identities such as Catalan’s, Simpson’s, d’ Ocagene’s etc.

Keywords


k-Pell Sequence, k- Pell-Lucas Sequence, Recurrence Relation.

References