• Title/Summary/Keyword: generalized Padovan number

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GENERALIZED PADOVAN SEQUENCES

  • Bravo, Jhon J.;Herrera, Jose L.
    • Communications of the Korean Mathematical Society
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    • v.37 no.4
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    • pp.977-988
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    • 2022
  • 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.