Bounds for the k-term Zeckendorf representations of Tribonacci-Lucas numbers with explicit results

Awaou Lare Ousseni; Japhet Odjoumani; Guy Degla

doi:10.2478/awutm-2026-0007

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Bounds for the k-term Zeckendorf representations of Tribonacci-Lucas numbers with explicit results

Annals of West University of Timisoara - Mathematics and Computer Science

Volume 62 (2026): Issue 1 (January 2026)

By: Awaou Lare Ousseni, Japhet Odjoumani and Guy Degla

Open Access

|Oct 2026

Abstract

Zeckendorf proved that every positive integer has a unique representation as a sum of non-consecutive Fibonacci numbers. In this paper, we applied the linear forms in logarithms to the Zeckendorf representation of the Tribonacci-Lucas sequences to find effective computable bounds for the representation. We then used a version of the Baker-Davenport reduction method to explicitly determine all the Tribonacci-Lucas numbers that admit a Zeckendorf representation into exactly five terms. We found that there are exactly two Tribonacci-Lucas, namely S₁₁ and S₁₄, that admit Zeckendorf representation into five terms.

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Articles in this issue

DOI: https://doi.org/10.2478/awutm-2026-0007 | Journal eISSN: 1841-3307 | Journal ISSN: 1841-3293

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Language: English

Page range: 72 - 91

Submitted on: Apr 18, 2026

Accepted on: Sep 30, 2026

Published online: Oct 13, 2026

Published in print: Jan 1, 2026

Published by: West University of Timisoara

In partnership with: Paradigm Publishing Services

Publication frequency: Volume open

Keywords:

recurrent sequences and Diophantine equations,

linear forms in logarithms,

reduction method

MSC:

11D61,

11D72,

11B39,

11B83,

11J86,

11D45,

11Y50

Related subjects:

Mathematics,

General mathematics

© 2026 Awaou Lare Ousseni, Japhet Odjoumani, Guy Degla, published by West University of Timisoara
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 62 (2026): Issue 1 (January 2026)