On Doubled and Quadrupled Fibonacci Type Sequences

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Yilmaz N. Ş. E., Włoch A., ÖZKAN E., Strzałka D.

Annales Mathematicae Silesianae, 2023 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2023
  • Doi Numarası: 10.2478/amsil-2023-0020
  • Dergi Adı: Annales Mathematicae Silesianae
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Anahtar Kelimeler: Fibonacci numbers, generalized Fibonacci numbers, generating function, Narayana's numbers, Padovan's numbers, Pascal's triangle
  • Marmara Üniversitesi Adresli: Hayır

Özet

In this paper we study a family of doubled and quadrupled Fibonacci type sequences obtained by distance generalization of Fibonacci sequence. In particular we obtain doubled Fibonacci sequence, doubled and quadrupled Padovan sequence and quadrupled Narayana's sequence. We give a binomial direct formula for these sequences using graph methods, and also we derive a number of identities. Moreover, we study matrix generators of these sequences and determine connections with the Pascal's triangle.