On F3(k, n) -numbers of the Fibonacci type

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Özkan E., Yilmaz N. Ş., Włoch A.

Boletin de la Sociedad Matematica Mexicana, vol.27, no.3, 2021 (ESCI, Scopus)

  • Publication Type: Article / Article
  • Volume: 27 Issue: 3
  • Publication Date: 2021
  • Doi Number: 10.1007/s40590-021-00381-9
  • Journal Name: Boletin de la Sociedad Matematica Mexicana
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, MathSciNet, zbMATH, DIALNET
  • Keywords: Generalized Fibonacci numbers, Narayana's numbers, Padovan's numbers, Generating function, Pascal's triangle
  • Open Archive Collection: AVESIS Open Access Collection
  • Erzincan Binali Yildirim University Affiliated: Yes

Abstract

© 2021, The Author(s).In this paper, we study a generalization of Narayana’s numbers and Padovan’s numbers. This generalization also includes a sequence whose elements are Fibonacci numbers repeated three times. We give combinatorial interpretations and a graph interpretation of these numbers. In addition, we examine matrix generators and determine connections with Pascal’s triangle.