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

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dc.contributor.authorDaşdemir, Ahmet
dc.contributor.authorBilgici, Göksal
dc.contributor.authorAhmed, Hossen
dc.date.accessioned2026-01-05T22:59:46Z
dc.date.issued2025-01-31
dc.description.abstractThe 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.
dc.description.urihttps://doi.org/10.54974/fcmathsci.1394995
dc.description.urihttps://dergipark.org.tr/tr/pub/fcmathsci/issue/90155/1394995
dc.identifier.doi10.54974/fcmathsci.1394995
dc.identifier.eissn2717-6185
dc.identifier.endpage33
dc.identifier.openairedoi_dedup___::4f1614f4c80226b6e43cf2f857f52e38
dc.identifier.orcid0000-0001-8352-2020
dc.identifier.orcid0000-0001-9964-5578
dc.identifier.orcid0000-0002-2358-9087
dc.identifier.startpage19
dc.identifier.urihttps://hdl.handle.net/20.500.12597/43500
dc.identifier.volume6
dc.publisherFundamentals of Contemporary Mathematical Sciences
dc.relation.ispartofFundamentals of Contemporary Mathematical Sciences
dc.rightsOPEN
dc.subjectAlgebra and Number Theory
dc.subjectCebir ve Sayı Teorisi
dc.subjectGeneralized order-k sequence
dc.subjectJacobsthal sequence
dc.subjecttrace of matrix
dc.subjectBinet
dc.subjectJacobsthal-Lucas sequence.
dc.titleOn the Generalized Order-k Jacobsthal and Jacobtshal-Lucas Numbers
dc.typeArticle
dspace.entity.typePublication
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