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Dergiler / Fundamentals of Contemporary Mathematical Sciences / 2026 / Volume: 6 Issue: 1

On the Generalized Order-k Jacobsthal and Jacobtshal-Lucas Numbers

Ahmet Daşdemir(KASTAMONU UNIVERSITY)0000-0001-8352-2020
Göksal Bilgici(KASTAMONU UNIVERSITY)0000-0001-9964-5578
Hossen Ahmed(Sebha University)0000-0002-2358-9087
Sayfa
—
Yayın Tarihi
2025-01-31
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Further, we investigate specific examples for our results and give special identities, i.e., sum formula and interrelationships between these sequences.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:The classic Jacobsthal numbers were generalized to k sequences of the generalized order-k Jacobsthal numbers and then have been studied by several authors.
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Temel Bulgular & Veri:In this paper, we explain that all of these studies used an incorrect version of order-k Jacobsthal numbers for reasons and give the correct definition of order-k Jacobsthal numbers.
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Sonuç & Katkı:Further, we investigate specific examples for our results and give special identities, i.e., sum formula and interrelationships between these sequences.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Generalized order-k sequence · Jacobsthal sequence · trace of matrix

Abstract

The classic Jacobsthal numbers were generalized to k sequences of the generalized order-k Jacobsthal numbers and then have been studied by several authors. In this paper, we explain that all of these studies used an incorrect version of order-k Jacobsthal numbers for reasons and give the correct definition of order-k Jacobsthal numbers. Further, we introduce the compatible generalized order-k Jacobsthal-Lucas numbers with the generalized order-k Jacobsthal numbers. Next, we give some properties of order-k Jacobsthal numbers and order-k Jacobsthal-Lucas numbers, including generating matrix, generalized Binet’s formula, and elementary matrix identities. Further, we investigate specific examples for our results and give special identities, i.e., sum formula and interrelationships between these sequences.

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Bu Makaleye Atıf Yap

Daşdemir, A., Bilgici, G., Ahmed, H. (2025). On the Generalized Order-k Jacobsthal and Jacobtshal-Lucas Numbers. Fundamentals of Contemporary Mathematical Sciences, Volume: 6 Issue: 1. https://doi.org/10.54974/fcmathsci.1394995

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