Special Cases of Generalized Leonardo Numbers : Modified p-Leonardo, p-Leonardo-Lucas and p-Leonardo Numbers
Open Access
- 15 December 2022
- journal article
- Published by Earthline Publishers in Earthline Journal of Mathematical Sciences
- Vol. 11 (2), 317-342
- https://doi.org/10.34198//ejms.11223.317342
Abstract
In this paper, we define and investigate modified p-Leonardo, p-Leonardo-Lucas and p-Leonardo sequences as special cases of the generalized Leonardo sequence. We present Binet's formulas, generating functions, Simson formulas, and the summation formulas for these sequences. Moreover, we give some identities and matrices related with these sequences. Furthermore, we show that there are close relations between modified p-Leonardo, p-Leonardo-Lucas, p-Leonardo numbers and Fibonacci, Lucas numbers.Keywords
This publication has 4 references indexed in Scilit:
- On Generalized Padovan NumbersPreprints.org, 2021
- Some Properties of Generalized Fibonacci Numbers: Identities, Recurrence Properties and Closed Forms of the Sum Formulas ∑nk=0 xkWmk+jArchives of Current Research International, 2021
- RELAÇÕES BIDIMENSIONAIS E IDENTIDADES DA SEQUÊNCIA DE LEONARDORevista Sergipana de Matemática e Educação Matemática, 2019
- A note on generalized Leonardo numbersNotes on Number Theory and Discrete Mathematics, 2019