This book presents the state-of-the-art results concerning recurrent sequences and their
practical applications in algebra, number theory, geometry of the complex plane, discrete …

In this paper, by considering the circulant matrix C n (H)= Circ (H k, 1, H k, 2,…, H k, n)
whose entries are the generalized k-Horadam numbers, we present a new generalization to …

In this work, we give new explicit solutions for the connection problems between generalized
Lucas polynomial sequence and the two polynomials, namely third and fourth kinds of …

In this work we solve in closed form the system of difference equations\begin {equation*} x_
{n+ 1}=\dfrac {ay_nx_ {n-1}+ bx_ {n-1}+ c}{y_nx_ {n-1}},\; y_ {n+ 1}=\dfrac {ax_ny_ {n-1}+ by …

The first main idea of this paper is to develop the matrix sequences that represent Padovan
and Perrin numbers. Then, by taking into account matrix properties of these new matrix …

In this paper, we present new upper and lower bounds for the spectral norm of an r-circulant
matrix H= C r (H k, 0, H k, 1, H k, 2,…, H k, n− 1) whose entries are the generalized k …

In this paper, we introduce a new family of the generalized $ k $-Leonardo numbers and
study their properties. We investigate the Gaussian Leonardo numbers and associated new …

In this paper, we define the Horadam hybrid quaternions and give some of their properties.
Moreover, we investigate the relations between the Fibonacci hybrid quaternions and the …

We apply the binomial transforms to Padovan and Perrin matrix sequences. Also, the Binet
formulas, summations, and generating functions of these transforms are found by recurrence …

Circulant matrices have important applications in solving ordinary differential equations. In
this paper, we consider circulant‐type matrices with the k‐Fibonacci and k‐Lucas numbers …