On the sequences of $(q,k)$-generalized Fibonacci numbers
Jean Lelis, Gersica Freitas, Alessandra Kreutz, Elaine Silva
Received March 6, 2023. Published online December 16, 2024.
Abstract: We consider a new family of recurrence sequences, the $(q,k)$-generalized Fibonacci numbers. These sequences naturally extend the well-known sequences of $k$-generalized Fibonacci numbers and generalized $k$-order Pell numbers. Further, we obtain the Binet formula and study the asymptotic behavior of the dominant root of the characteristic equation. The proof methods exploit pairs of characteristic polynomials which allow several auxiliary results.
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Affiliations: Jean Lelis (corresponding author), Faculdade de Matemática/ ICEN/UFPA, Belém - PA, 66075-110 Brazil, e-mail: jeanlelis@ufpa.br; Gersica Freitas, Unidade Acadêmica de Cabo de Santo Agostinho, Universidade Federal Rural de Pernambuco, Cabo de Santo Agostinho - PE, 3320 6000 Brazil, e-mail: gersica.freitas@ufrpe.br; Alessandra Kreutz, Instituto Federal de Brasília, Campus Taguatinga, 70.910-900 Brasília - DF, Brazil, e-mail: alessandra.kreutz@ifb.edu.br; Elaine Silva, Instituto de Matemática, Universidade Federal de Alagoas, 57072-970 Maceió - AL, Brazil, email: elaine.silva@im.ufal.br
