ON DOUBLED AND QUADRUPLED FIBONACCI TYPE SEQUENCES

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

Annales Mathematicae Silesianae, vol.38, no.2, pp.336-350, 2024 (ESCI, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 38 Issue: 2
  • Publication Date: 2024
  • Doi Number: 10.2478/amsil-2023-0020
  • Journal Name: Annales Mathematicae Silesianae
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.336-350
  • Keywords: Fibonacci numbers, generalized Fibonacci numbers, generating function, Narayana’s numbers, Padovan’s numbers, Pascal’s triangle
  • Open Archive Collection: AVESIS Open Access Collection
  • Marmara University Affiliated: Yes

Abstract

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.