<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

Online veröffentlicht: 22. Nov. 2023

Seitenbereich: -

Eingereicht: 20. Jan. 2023

Akzeptiert: 07. Nov. 2023

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

Schlüsselwörter
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

Online veröffentlicht: 22. Nov. 2023

Seitenbereich: -

Eingereicht: 20. Jan. 2023

Akzeptiert: 07. Nov. 2023

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

SchlüsselwörterFibonacci 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.

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