On repunit polynomials sequence
DOI:
https://doi.org/10.14393/BEJOM-v5-2024-72280Keywords:
Polynomial repunit, repunit number, sequenceAbstract
In this paper, we define a sequence of polynomials associated with the repunit numerical sequence. This involves extending the concept of the repunit sequence, a sequence type Horadam, represented by the sequence of repunit numbers, where rₙ represents the n-th repunit, and the recurrence relation: rₙ₊₁ = 11rₙ-10rₙ₋₁, with r₀ = 0, r₁ = 1 for n ≥ 1. In this paper, we investigate this new polynomial sequence in detail and present some results and applications derived from this investigation. For instance, we study the characteristic equation and derive the corresponding generating function. Additionally, we analyze the recurrence relation associated with the sum of n repunit polynomials.
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Copyright (c) 2024 Eudes Antonio Costa, Fernando Soares de Carvalho
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