TY  - JOUR
T1  - Catalan Transform of The k-Lucas Numbers
TT  - Catalan Transform of The 𝒌−Lucas Numbers
AU  - Taştan, Merve
AU  - Özkan, Engin
AU  - Güngör, Olcay
PY  - 2020
DA  - February
DO  - 10.18185/erzifbed.638488
JF  - Erzincan University Journal of Science and Technology
PB  - Erzincan Binali Yıldırım Üniversitesi
WT  - DergiPark
SN  - 2149-4584
SP  - 145
EP  - 149
VL  - 13
IS  - ÖZEL SAYI I
LA  - tr
AB  - Buçalışmada, k-LucasdizisininCatalandönüşümününtanımıverildi. k-LucasdizisininCatalandönüşümününgerenfonksiyonu elde edildi.Ayrıca,Hankelfonksiyonu kullanılarakoluşturulanmatrislerin determinantları hesaplandı.
KW  - k-Lucas dizisi
KW  - k-Fibonacci dizisi
KW  - Catalan dönüşümü
KW  - Hankel dönüşümü.
N2  - 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.
CR  - [1]	Barry, P. (2005), A Catalan transform and related transformations on integer sequences. J.Integer Seq., 8(4), 1-24.
CR  - [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.
CR  - [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.
UR  - https://doi.org/10.18185/erzifbed.638488
L1  - https://dergipark.org.tr/tr/download/article-file/986580
ER  -