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Research Article Open access CC BY 4.0

On Binomial Transform of the Generalized Fifth Order Pell Sequence

Yüksel Soykan

Asian Journal of Advanced Research and Reports · pp. 8–29 · Published 13 Dec 2021

10.9734/ajarr/2021/v15i930423

Abstract

In this paper, we define the binomial transform of the generalized fifth order Pell sequence and as special cases, the binomial transform of the fifth order Pell and fifth order Pell-Lucas sequences will be introduced. We investigate their properties in details. We present Binet’s formulas, generating functions, Simson formulas, recurrence properties, and the summation formulas for these binomial transforms. Moreover, we give some identities and matrices related with these binomial transforms.

Binomial transform fifth order Pell Sequence fifth order Pell numbers binomial transform of fifth order Pell Sequence binomial transform of fifth order Pell-Lucas sequence

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Cited by 4

On Various Binomial Transforms of the Generalized Pell Matrix Sequences

Sukran Uygun, Ozan Haklıdır · Journal of new theory · 2025

The Properties of Binomial Transforms for Modified (s,t)-Pell Matrix Sequence

Sukran Uygun, Ozan Haklıdır · Communications in Advanced Mathematical Sciences · 2024

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