In this paper we consider the sequence of Leonardo numbers and we present some
properties involving this sequence, including the Binet formula and the generating function …

In this article, we find elements of the Lucas polynomials by using two matrices. We extend
the study to the n-step Lucas polynomials. Then the Lucas polynomials and their …

From Binet's formula of Mersenne sequence we get some properties for this sequence.
Mersenne, Jacobsthal and Jacobsthal-Lucas sequences are considered in order to achieve …

In this paper, we introduce a new quadruple number sequence by means of Leonardo
numbers, which we call ordered Leonardo quadruple numbers. We determine the properties …

In this paper, we introduce the split k-Fibonacci and k-Lucas quaternions. We obtain the
Binet formulas, generating functions and exponential generating functions of these …

Some arithmetic properties of the generalized Lucas sequences are studied, extending a
number of recent results obtained for Fibonacci, Lucas, Pell, and Pell–Lucas sequences …

97 A NOTE ON k-PELL, k-PELL-LUCAS AND MODIFIED k-PELL NUMBERS WITH
ARITHMETIC INDEXES 1. Introduction In this paper, we consider Page 1 Acta Math. Univ …

SOME PROPERTIES OF THE GENERALIZED FIBONACCI SEQUENCE {qn} BY MATRIX
METHODS Sang Pyo Jun and Kwang Ho Choi 1. Introduction For Page 1 Korean J. Math …

The Fibonacci sequence is a well-known example of second order recurrence sequence,
which belongs to a particular class of recursive sequences. In this article, other generalized …

Abstract Number sequences have been the subject of several research studies. From the
algebraic properties to the generating matrices and generating functions of these …