Work

On Tricomplex Horadam Numbers: A New Class of Horadam Sequences

Year: 2025

Type: article

Abstract: This study introduces an innovative approach to Horadam sequences. The aim of this paper is to investigate the Tricomplex Horadam sequence and its properties. It begins with the tricomplex ring T and key results related to Horadam-type sequences. The Tricomplex Horadam sequence is then defined, with a discussion of its properties, the Binet formula, and the generating function in vector form. Next, several fundamental identities, including the Tagiuri–Vajda and d’Ocagne identities, are examined, along with their implications and examples from previous Tricomplex Horadam-type sequences. Finally, the sum of terms associated with the Tricomplex Horadam sequence is presented. The research problem consists in determining properties symmetrical or analogous to the Horadam-type sequence for the Tricomplex Horadam sequence.

Source: Symmetry

DOI: 10.3390/sym17101616

Authors: Douglas C. Santos, Paula M. M. C. Catarino, Eudes A. Costa

Institutions: University of Trás-os-Montes and Alto Douro, Universidade Federal do Tocantins

Language: English

Topic: Advanced Mathematical Theories and Applications

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funder: Universidade Federal do Tocantins