As relações recorrentes n-dimensionais de Leonardo
DOI:
https://doi.org/10.5902/2179460X64802Keywords:
Complexificação, relações n-dimensionais, sequência de Leonardo.Abstract
A sequência de Leonardo é uma sequência pouco conhecida, porém apresenta semelhanças com a sequência de Fibonacci. Dessa
forma, prevalece os termos iniciais, diferindo apenas a relação de recorrência, a qual foi adicionado o valor 1 na recorrência
de Leonardo. Com isso, este trabalho apresenta uma discussão referente às relações recorrentes n-dimensionais, com base noo
modelo recursivo unidimensional Le(n) = Le(n−1) + Le(n−2) + 1, ∀n ∈ N, com Le(0) = Le(1) = 1 sendo os seus termos iniciais.
A partir do processo de complexificação da sequência de Leonardo, são descritas as propriedades matemáticas dos números
bidimensionais (Le(n,m)), tridimensionais (Le(n,m,p)) e n-dimensionais (Le(n,n2,n3, · · · , nn)) de Leonardo, permitindo-nos
explorar propriedades e sua extensão para os inteiros.
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