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http://dx.doi.org/10.4134/CKMS.c210367

GENERALIZED PADOVAN SEQUENCES  

Bravo, Jhon J. (Departamento de Matematicas Universidad del Cauca)
Herrera, Jose L. (Departamento de Matematicas Universidad del Cauca)
Publication Information
Communications of the Korean Mathematical Society / v.37, no.4, 2022 , pp. 977-988 More about this Journal
Abstract
The Padovan sequence is the third-order linear recurrence (𝓟n)n≥0 defined by 𝓟n = 𝓟n-2 + 𝓟n-3 for all n ≥ 3 with initial conditions 𝓟0 = 0 and 𝓟1 = 𝓟2 = 1. In this paper, we investigate a generalization of the Padovan sequence called the k-generalized Padovan sequence which is generated by a linear recurrence sequence of order k ≥ 3. We present recurrence relations, the generalized Binet formula and different arithmetic properties for the above family of sequences.
Keywords
Fibonacci number; generalized Padovan number; recurrence sequence;
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Times Cited By KSCI : 1  (Citation Analysis)
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