A note on the coefficient array of a generalized Fibonacci polynomial

A. G. Shannon and Ömür Deveci
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367-8275
Volume 26, 2020, Number 4, Pages 206–212
DOI: 10.7546/nntdm.2020.26.4.206-212
Full paper (PDF, 156 Kb)

Details

Authors and affiliations

A. G. Shannon
Warrane College, the University of New South Wales
Kensington, NSW 2033, Australia

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

Abstract

A particular version of a Fibonacci polynomial is presented and the coefficients are tabulated to bring out some of their number theory properties with known results. Generalizations of the fundamental and primordial Lucas sequences are used in the proofs.

Keywords

• Fibonacci numbers and polynomials
• Lucas numbers
• Bernoulli polynomials
• Falling factorial coefficients
• Umbral calculus.

2010 Mathematics Subject Classification

• 11B39
• 11B68

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