The main object of this paper is to introduce and investigate some properties and relations involving sequences of numbers Fn,m(r), for m = 2, 3, 4, and r is some real number. These sequences are generalizations of the Jacobsthal and Jacobsthal Lucas numbers.

In this paper, we present a generalization of well-known k-Fibonacci sequence. Namely, defined generalized This sequence generalizes others, sequence, classical Fibonacci Pell and Jacobsthal We establish some the interesting properties Also, obtain generating function for them.

The bi-periodic Fibonacci sequence also known as the generalized Fibonacci sequence was fırst introduced into literature in 2009 by Edson and Yayenie [9] after which the bi-periodic Lucas sequence was defined in a similar fashion in 2004 by Bilgici [5]. In this study, we introduce a new generalization of the Jacobsthal numbers which we shall call bi-periodic Jacobsthal sequences similar to the ...

We give an explicit evaluation, in terms of products of Jacobsthal numbers, of the Hankel determinants of order a power of two for the period-doubling sequence. We also explicitly give the eigenvalues and eigenvectors of the corresponding Hankel matrices.

In this study, we define the Jacobsthal Lucas E-matrix and R-matrix alike to the Fibonacci Q-matrix. Using this matrix represantation we have found some equalities and Binet-like formula for the Jacobsthal and Jacobsthal-Lucas numbers.

Gaussian Jacobsthal-Padovan numbers have been the central focus of this paper and firstly number sequence has defined. Later, we given proof generating function sequence. After that by using function, Binet formula for Additionally, investigated some properties such as Simson identity, summation formulas Finally, obtained matrices whose elements are numbers.

In this paper, we define the Fibonacci–Jacobsthal, Padovan–Fibonacci, Pell–Fibonacci, Pell–Jacobsthal, Padovan–Pell and Padovan–Jacobsthal sequences which are directly related with Fibonacci, Jacobsthal, Pell Padovan numbers give their structural properties by matrix methods. Then obtain new relationships between numbers.

Abstract In this paper we investigate upper and lower bounds of the norms of the circulant matrices whose elements are k−Jacobsthal numbers and k−Jacobsthal Lucas numbers.