On Doubled and Quadrupled Fibonacci Type Sequences

Nur Şeyma Yilmaz; Andrzej Włoch; Engin Özkan; Dominik Strzałka

doi:10.2478/amsil-2023-0020

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On Doubled and Quadrupled Fibonacci Type Sequences

Annales Mathematicae Silesianae

Volume 38 (2024): Issue 2 (September 2024)

By: Nur Şeyma Yilmaz, Andrzej Włoch , Engin Özkan and Dominik Strzałka

Open Access

|Nov 2023

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.

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Articles in this issue

DOI: https://doi.org/10.2478/amsil-2023-0020 | Journal eISSN: 2391-4238 | Journal ISSN: 0860-2107

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Language: English

Page range: 336 - 350

Submitted on: Jan 20, 2023

Accepted on: Nov 7, 2023

Published on: Nov 22, 2023

Published by: University of Silesia in Katowice, Institute of Mathematics

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

Fibonacci numbers,

Padovan’s numbers,

generalized Fibonacci numbers,

Related subjects:

© 2023 Nur Şeyma Yilmaz, Andrzej Włoch, Engin Özkan, Dominik Strzałka, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 38 (2024): Issue 2 (September 2024)