Fibonacci Cartan and Lucas Cartan numbers

Öztürk İ., Çakır H.

OPEN MATHEMATICS, cilt.23, sa.1, ss.1-13, 2025 (SCI-Expanded)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 23 Sayı: 1
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1515/math-2025-0204
  • Dergi Adı: OPEN MATHEMATICS
  • Derginin Tarandığı İndeksler: Scopus, Science Citation Index Expanded (SCI-EXPANDED), MathSciNet, zbMATH, Directory of Open Access Journals
  • Sayfa Sayıları: ss.1-13
  • Recep Tayyip Erdoğan Üniversitesi Adresli: Evet

Özet

This study introduces Fibonacci Cartan and Lucas Cartan numbers, extending the classical Fibonacci and Lucas sequences into the framework of Cartan numbers. By leveraging algebraic and geometric properties, we establish recurrence relations, generating functions, Binet-like formulas, and fundamental identities such as Catalan's, Cassini's, and d'Ocagne's identities for these novel number sequences. Furthermore, summation formulas and additional properties are explored to provide a comprehensive mathematical characterization. The findings contribute to the ongoing development of number theory and its applications in algebra and geometry.