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.
Kaynakça
- [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.
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] 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.
Ayrıntılar
| Birincil Dil | Türkçe |
|---|---|
| Konular | Mühendislik |
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 28 Şubat 2020 |
| Yayımlandığı Sayı | Yıl 2020 |