On the connections between Pell numbers and Fibonacci
p-numbers

Anthony G. Shannon, Özgür Erdağ and Ömür Deveci
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 27, 2021, Number 1, Pages 148–160
DOI: 10.7546/nntdm.2021.27.1.148-160
Full paper (PDF, 235 Kb)

Details

Authors and affiliations

Anthony G. Shannon
Warrane College, University of New South Wales
Kensington, Australia

Özgür Erdağ
Department of Mathematics, Faculty of Science and Letters
Kafkas University 36100, Turkey

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

Abstract

In this paper, we define the Fibonacci–Pell p-sequence and then we discuss the connection of the Fibonacci–Pell p-sequence with the Pell and Fibonacci p-sequences. Also, we provide a new Binet formula and a new combinatorial representation of the Fibonacci–Pell p-numbers by the aid of the n-th power of the generating matrix of the Fibonacci–Pell p-sequence. Furthermore, we derive relationships between the Fibonacci–Pell p-numbers and their permanent, determinant and sums of certain matrices.

Keywords

• Pell sequence
• Fibonacci p-sequence
• Matrix
• Representation

2010 Mathematics Subject Classification

• 11K31
• 11C20
• 15A15

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