On intercalated Fibonacci sequences

Krassimir T. Atanassov and Anthony G. Shannon
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 26, 2020, Number 3, Pages 218–223
DOI: 10.7546/nntdm.2020.26.3.218-223
Full paper (PDF, 81 Kb)

Details

Authors and affiliations

Krassimir T. Atanassov
Department of Bioinformatics and Mathematical Modelling
IBPhBME, Bulgarian Academy of Sciences
Acad. G. Bonchev Str., Bl. 105, Sofia–1113, Bulgaria

Anthony G. Shannon
Warrane College, The University of New South Wales
356 Anzac Parade, Kensington, NSW 2033, Australia

Abstract

We construct three intercalated sequences and develop their essential properties which are generalizations of the three basic Fibonacci sequences. They are extensions of pulsated sequences described at previous Fibonacci conferences. We relate these sequences to the sequence {y_n}_{n ≥ 0} = {0, 1, 4, 15, 56, …}.

Keywords

• Fibonacci-type sequences
• Recurrence relations
• Induction
• Horadam sequences

2010 Mathematics Subject Classification

• 11B37
• 11B39

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