Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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GENERALIZED PADOVAN SEQUENCES

  • Bravo, Jhon J. (Departamento de Matematicas Universidad del Cauca) ;
  • Herrera, Jose L. (Departamento de Matematicas Universidad del Cauca)
  • Received : 2021.11.05
  • Accepted : 2022.04.22
  • Published : 2022.10.01
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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

Acknowledgement

The first author was supported in part by Project VRI ID 5385 (Universidad del Cauca).

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