<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</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.

On Doubled and Quadrupled Fibonacci Type Sequences

Erzincan Binali Yıldırım University, Faculty of Arts and Sciences

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"On Doubled and Quadrupled Fibonacci Type Sequences"}

In this paper we study a family of doubled and quadrupled Fibonacci type sequences obtained by distance generalization of Fibonacci sequence. In particular we...

On Doubled and Quadrupled Fibonacci Type Sequences

Published Online: Nov 22, 2023

Page range: -

Received: Jan 20, 2023

Accepted: Nov 07, 2023

DOI: https://doi.org/10.2478/amsil-2023-0020

Keywords
Fibonacci numbers, Padovan’s numbers, generalized Fibonacci numbers, Narayana’s numbers, generating function, Pascal’s triangle

© 2023 Nur Şeyma Yilmaz et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

On Doubled and Quadrupled Fibonacci Type Sequences

Published Online: Nov 22, 2023

Page range: -

Received: Jan 20, 2023

Accepted: Nov 07, 2023

DOI: https://doi.org/10.2478/amsil-2023-0020

KeywordsFibonacci numbers, Padovan’s numbers, generalized Fibonacci numbers, Narayana’s numbers, generating function, Pascal’s triangle

© 2023 Nur Şeyma Yilmaz et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
Fibonacci numbers, Padovan’s numbers, generalized Fibonacci numbers, Narayana’s numbers, generating function, Pascal’s triangle