Elen Viviani Pereira SPREAFICO, Paula Maria Machado Cruz CATARINO, Eudes Antonio COSTA
Received September 1, 2025. Published online May 21, 2026.
Abstract: This article introduces a new generalization of Leonardo numbers called the tricomplex Leonardo numbers. Some properties, such as the recurrence relation and relations with the tricomplex Fibonacci and tricomplex Lucas numbers, are provided. Moreover, the Binet formula and the generating function are stated. In addition, some identities such as Tagiuri-Vajda's, d'Ocagne's, Cassini's, and Catalan's identities are established.
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Affiliations: Elen Viviani Pereira Spreafico, Institute of Mathematics, Federal University of Mato Grosso do Sul, Avenida Senador Filinto Müller, 1555, Campo Grande, 79060-300, Brazil, e-mail: elen.spreafico@ufms.br; Paula Maria Machado Cruz Catarino, Department of Mathematics, University of Trás-os-Montes e Alto Douro, Vila Real, 5001-801, Portugal, e-mail: pcatarin@utad.pt; Eudes Antonio Costa (corresponding author), Department of Mathematics, Federal University of Tocantins, Arraias, Tocantins, 77330-000, Brazil, e-mail: eudes@uft.edu.br
