In this study, a generalization of the sequence of balancing numbers called as k-balancing
numbers is considered and some of their properties are established. Further, the balancing …

The terms balancing numbers and Lucas-balancing numbers are used to describe the
series of numbers generated by the recursive formulas Bn= 6Bn− 1− Bn− 2; B0= 0, B1= 1 …

In this paper, we introduce and study balancing hybrinomials, ie, polynomials being a
generalization of balancing hybrid numbers. We provide some properties of the balancing …

In this paper, we define and investigate the generalized Edouard sequences and we deal
with, in detail, two special cases, namely, Edouard and Edouard-Lucas sequences. We …

In this paper, we investigate properties of the generalized balancing sequence and we deal
with, in detail, namely, balancing, modified Lucas-balancing and Lucas-balancing …

In this paper, we introduce a operator in order to derive some new symmetric properties of
(p, q)-modified Pell numbers and we give some new generating functions of the products of …

We study properties of generalized balancing numbers. We start with some basic identities.
Thereafter, we focus on connections to generalized Fibonacci numbers. Using generating …

Let us define the r-circulant matrix C r= C ircr (c 0, c 1, c 2,…, cn-1) such that the entries of C
r are ci= B k, s+ it or ci= C k, s+ it, where B k, s+ it and C k, s+ it are k-balancing and k-Lucas …

Quaternions and split quaternions are used in quantum physics, computer science, and in
many areas of mathematics. In this paper, we define and study two new classes of split …

In this study, we define the binomial transforms of balancing and Lucas-balancing
polynomials. Also, the generating functions, Binet formulas, and summations of these …