Catalan Transform of The 𝒌−Lucas Numbers

Year 2020, Volume: 13 Issue: ÖZEL SAYI I, 145 - 149, 28.02.2020

Engin Özkan , Merve Taştan , Olcay Güngör

https://doi.org/10.18185/erzifbed.638488

Cited By: 3

Abstract

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.

Keywords

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

Catalan Transform of The k-Lucas Numbers

Abstract

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.

Keywords

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

References

• [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.