Published: 2023-11-22

On doubled and quadrupled Fibonacci type sequences

Nur Şeyma Yilmaz , Andrzej Włoch Logo ORCID , Engin Özkan , Dominik Strzałka

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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Yilmaz, N. Şeyma, Włoch, A., Özkan, E., & Strzałka, D. (2023). On doubled and quadrupled Fibonacci type sequences. Annales Mathematicae Silesianae, 38(2), 336–350. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/16395

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Vol. 38 No. 2 (2024)
Published: 2024-07-23


ISSN: 0860-2107
eISSN: 2391-4238
Ikona DOI 10.1515/amsil

Publisher
University of Silesia Press

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