In this paper, new families of generalized Fibonacci and Lucas numbers are introduced. In addition, we present the recurrence relations and the generating functions of the new families for $k=2$.

Given the generalized Fibonacci sequence {Wn(a, b; p, q)} we can naturally associate a matrix of order 2, denoted by W(p, q), whose coefficients are integer numbers. In this paper, using this matrix,… Expand

This is a survey on certain results which bring about a connection between Fibonacci sequences on the one hand and the areas of matrix theory and quantum information theory, on the other.

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… Expand

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… Expand

In this manuscript, a new family of k- Gaussian Fibonacci numbers has been identified and some relationships between this family and known Gaussian Fibonacci numbers have been found. Also, I the… Expand

. By interpreting various sums involving Fibonacci and Lucas numbers physically, we show how one can often generate an additional summation with little eﬀort. To illustrate the fruitfulness of the… Expand

Difference equations of the form (2) are expressible in a matrix form analogous to (1) and may be viewed as the solution to n+2 ~ n + n+l which has initial terms uQ = 0 and u1 = 1.Expand