On a generalization of the Pell sequence

Autor:	Florian Luca, José Luis Arciniegas Herrera, Jhon J. Bravo
Rok vydání:	2020
Předmět:	Combinatorics Recurrence relation Fibonacci number Generalization generalized fibonacci number QA1-939 Order (ring theory) recurrence sequence Recurrence sequence generalized pell number Mathematics Pell number
Zdroj:	Mathematica Bohemica Mathematica Bohemica, Vol 146, Iss 2, Pp 199-213 (2021)
DOI:	10.21136/mb.2020.0098-19
Popis:	The Pell sequence $(P_n)_{n=0}^{\infty }$ is the second order linear recurrence defined by $P_n=2P_{n-1}+P_{n-2}$ with initial conditions $P_0=0$ and $P_1=1$. In this paper, we investigate a generalization of the Pell sequence called the $k$-generalized Pell sequence which is generated by a recurrence relation of a higher order. We present recurrence relations, the generalized Binet formula and different arithmetic properties for the above family of sequences. Some interesting identities involving the Fibonacci and generalized Pell numbers are also deduced.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4e15ac962b7baf689d3b3e26a53bd1a9 https://doi.org/10.21136/mb.2020.0098-19 Zobrazit plný text záznamu