On Generalized Pell Numbers of Order r ≥ 2

E. V. Pereira Spreafico, M. Rachidi

Abstract


In this paper we investigate the generalized Pell numbers of order r ≥ 2 through the properties of their related fundamental system of generalized Pell numbers. That is, the generalized Pell number of order r ≥ 2; are expressed as a linear combination of a fundamental system of generalized Pell numbers. The properties of this fundamental system are examined and results can be established for generalized Pell numbers of order r ≥ 2. Some identities and combinatorial results are established. Moreover, the analytic study of the fundamental system of generalized Pell is provided. Furthermore, the generalized Pell Cassini identity type is provided.


Keywords


Generalized Pell fundamental system; Generalized Pell numbers; Combinatorial identities; Analytic representations; Generalized Cassini identity

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DOI: https://doi.org/10.5540/tcam.2021.022.01.00125

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Trends in Computational and Applied Mathematics

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