Catalan Transform of The 𝒌−Lucas Numbers

Öz

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.

Anahtar Kelimeler

• 𝑘−Lucas sequence,𝑘−Fibonacci sequence,Catalan Transform,Hankel Transform.

Catalan Transform of The k-Lucas Numbers

Öz

Bu çalışmada, k-Lucas dizisinin Catalan dönüşümünün tanımı verildi. k-Lucas dizisinin Catalan dönüşümünün geren fonksiyonu elde edildi. Ayrıca, Hankel fonksiyonu kullanılarak oluşturulan matrislerin determinantları hesaplandı.

Anahtar Kelimeler

• k-Lucas dizisi,k-Fibonacci dizisi,Catalan dönüşümü,Hankel dönüşümü.

Kaynakça

1. [1] Barry, P. (2005), A Catalan transform and related transformations on integer sequences. J.Integer Seq., 8(4), 1-24.
2. [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.
3. [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.