A new family of Gauss (k,t)-Horadam numbers

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Taştan M., Yılmaz N., Özkan E.

ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, cilt.15, sa.12, ss.22502254, 2022 (ESCI, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 15 Sayı: 12
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1142/s1793557122502254
  • Dergi Adı: ASIAN-EUROPEAN JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, zbMATH
  • Sayfa Sayıları: ss.22502254
  • Anahtar Kelimeler: Cassini identity, Fibonacci number, Gauss number, generating function, Horadam number
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Marmara Üniversitesi Adresli: Hayır

Özet

We present a new family of Gauss [Formula: see text]-Horadam numbers and obtain Binet formula of this family. We give the relationship between this family and the known Gauss [Formula: see text]-Horadam number. Then we prove the Cassini and Catalan identities for this family. Furthermore, we investigate the sums, the recurrence relations and generating functions of this family.