On the connections among Fibonacci, Pell, Jacobsthal and Padovan numbers

Ömür Deveci
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 27, 2021, Number 2, Pages 111–128
DOI: 10.7546/nntdm.2021.27.2.111-128
Full paper (PDF, 248 Kb)

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Authors and affiliations

Ömür Deveci
Department of Mathematics, Faculty of Science and Letters,
Kafkas University, 36100, Turkey

Abstract

In this paper, we define the Fibonacci–Jacobsthal, Padovan–Fibonacci, Pell–Fibonacci, Pell–Jacobsthal, Padovan–Pell and Padovan–Jacobsthal sequences which are directly related with the Fibonacci, Jacobsthal, Pell and Padovan numbers and give their structural properties by matrix methods. Then we obtain new relationships between Fibonacci, Jacobsthal, Pell and Padovan numbers.

Keywords

• Fibonacci sequence
• Jacobsthal sequence
• Pell sequence
• Padovan sequence
• Matrix
• Representation

2020 Mathematics Subject Classification

• 11K31
• 11C20
• 15A15

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