Erzincan University Journal of Science and Technology 2149-4584 Erzincan Binali Yildirim University 10.18185/erzifbed.638488 Engineering Mühendislik Catalan Transform of The 𝒌−Lucas Numbers Catalan Transform of The k-Lucas Numbers https://orcid.org/0000-0002-4188-7248 Özkan Engin ERZİNCAN BİNALİ YILDIRIM ÜNİVERSİTESİ FEN EDEBİYAT FAKÜLTESİ TARİHİ BÖLÜMÜ https://orcid.org/0000-0002-6001-8267 Taştan Merve ERZİNCAN BİNALİ YILDIRIM ÜNİVERSİTESİ, FEN BİLİMLERİ ENSTİTÜSÜ https://orcid.org/0000-0003-1758-9862 Güngör Olcay ERZINCAN UNIVERSITY 02 28 2020 13 ÖZEL SAYI I 145 149 10 25 2019 02 21 2020 Copyright © 2008, Erzincan University Journal of Science and Technology 2008 Erzincan University Journal of Science and Technology

In this study, the 𝐶𝐿𝑘,𝑛 description of Catalan transformation of 𝑘−Lucas 𝐿𝑘,𝑛 sequences was given. The 𝐶𝐿𝑘,𝑛 generating function of Catalan transformation of 𝑘−Lucas 𝐿𝑘,𝑛 sequences was obtained. And also, 𝐶𝐿𝑘,𝑛 transformation was written as the multiplying of Catalan matris C which is the lower triangular matris, and the 𝐿𝑘 matris of 𝑛 𝑥 1 type. Determinants of matrices which were formed with 𝐶𝐿𝑘,𝑛 by using Hankel transform were calculated.

Buçalışmada, k-LucasdizisininCatalandönüşümününtanımıverildi. k-LucasdizisininCatalandönüşümününgerenfonksiyonu elde edildi.Ayrıca,Hankelfonksiyonu kullanılarakoluşturulanmatrislerin determinantları hesaplandı.

 k-Lucas dizisi k-Fibonacci dizisi Catalan dönüşümü Hankel dönüşümü. 𝑘−Lucas sequence 𝑘−Fibonacci sequence Catalan Transform Hankel Transform. [1] Barry, P. (2005), A Catalan transform and related transformations on integer sequences. J.Integer Seq., 8(4), 1-24. [2] Cvetkovi´c, A., Rajkovi´c, R., and Ivkovi´c, M. (2002), Catalan numbers, and Hankel transform, and Fibonacci numbers. J. Integer Seq. 5(1), 1-8. [9] Özkan, E., Taştan, M., Aydoğdu, A , (2018), 2-Fibonacci Polynomials in the Family of Fibonacci Numbers, Notes on Number Theory and Discrete Mathematics, 24, 47-55.