Catalan Transform of the k-Mersenne and k-Mersenne-Lucas Sequences

Creative Commons License

Şen B., Uysal M., Özkan E.

3 th International Symposium on Current Developments in Fundamental and Applied Mathematics Sciences (ISCDFAMS -2024), İstanbul, Türkiye, 2 - 05 Eylül 2024, ss.56-57, (Özet Bildiri)

  • Yayın Türü: Bildiri / Özet Bildiri
  • Basıldığı Şehir: İstanbul
  • Basıldığı Ülke: Türkiye
  • Sayfa Sayıları: ss.56-57
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Erzincan Binali Yıldırım Üniversitesi Adresli: Evet

Özet

In this study, we examine an application of k-Mersenne and k-mersenne-Lucas sequences. We

present the Catalan transformations of k-Mersenne and k-mersenne-Lucas sequences and give the

properties of these Catalan transformations. Catalan transformations of k-Mersenne and k-Mersenne-Lucas

sequences have terms according to different values of k, and some of them are associated with the sequences

in OEIS. Moreover, we apply the Hankel transform to the Catalan transformations of k-Mersenne and k-

mersenne-Lucas sequences. We obtain the generating functions of the Catalan transformation of k-

Mersenne and k-Mersenne-Lucas sequences. Finally, the determinants of the created matrices are calculated

by applying the Hankel transform to the terms of the Catalan transformations of the k-Mersenne and k-

Mersenne-Lucas sequences.