On the Incomplete Edouard and Incomplete Edouard–Lucas Numbers

Elen Viviani Pereira Spreafico (), Eudes Antonio Costa and Paula Catarino
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Elen Viviani Pereira Spreafico: Institute of Mathematics, Federal University of Mato Grosso do Sul, Campo Grande 79060-300, Brazil
Eudes Antonio Costa: Department of Mathematics, Federal University of Tocantins, Arraias 77330-000, Brazil
Paula Catarino: Department of Mathematics, University of Trás-os-Montes e Alto Douro, 5001-801 Vila Real, Portugal

Mathematics, 2024, vol. 12, issue 21, 1-9

Abstract: This study introduces two new sequences: the incomplete Edouard and the incomplete Edouard–Lucas numbers. In addition, we establish some of the properties, identities, and recurrence relations of these sequences. The relations of these new sequences with balancing, Lucas-balancing, incomplete balancing, and incomplete Lucas-balancing numbers are explored, and some new identities are provided. Moreover, the functions for generating the incomplete Edouard and incomplete Edouard–Lucas numbers are stated.

Keywords: incomplete sequences; Edouard numbers; Edouard–Lucas numbers; balancing numbers; Lucas-balancing numbers; combinatorial expressions; analytic representations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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