Work

Some Properties of the Multi-Figurate Numbers That Are Simultaneously Triangular and Centered Triangular

Year: 2026

Type: article

Abstract: A study of the multi-figurate numbers that are simultaneously triangular and centered triangular is presented. Starting from the generalized Pell equation associated with this class of multi-figurate numbers, we describe the corresponding sequence and investigate its algebraic properties. In particular, we obtain a companion matrix representation for the sequence. In addition, we derive several identities of Tagiuri–Vajda, Catalan, Cassini, and d’Ocagne types satisfied by this sequence. These results provide a systematic description of the algebraic structure associated with the sequence of numbers that are simultaneously triangular and centered triangular.

Source: Communications in Advanced Mathematical Sciences

DOI: 10.33434/cams.2016687

Authors: Francisco Hedyleno Coelho Bezerra, Francisco Regis Vieira Alves, Eudes Antonio Costa

Institutions: Instituto Federal de Educação, Ciência e Tecnologia do Ceará, 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: diamond

OpenAlex ID: W7223985576

FWCI:

Cites: 14

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Related to: 10