Dursun Tasci

On the order-k generalized Lucas numbers

In this paper we give a new generalization of the Lucas numbers in matrix representation. Also we present a relation between the generalized order-k Lucas sequences and Fibonacci sequences.

Incomplete Fibonacci and Lucas p-numbers

In this article, we define the incomplete Fibonacci and Lucas p-numbers, we study the recurrence relations and some properties of these numbers.

A sequence of upper bounds for the Perron root of a nonnegative matrix

Abstract We present a sequence of progressively better upper bounds for the Perron root of a nonnegative matrix. Each element in the sequence is a function of the Perron root of the arithmetic symmetrization of a power of the matrix. The results complement those of Szyld based on the geometric symmetrization of a power of the matrix.

Vieta-Pell and Vieta-Pell-Lucas polynomials

In the present paper, we introduce the recurrence relation of Vieta-Pell and Vieta-Pell-Lucas polynomials. We obtain the Binet form and generating functions of Vieta-Pell and Vieta-Pell-Lucas polynomials and define their associated sequences. Moreover, we present some differentiation rules and finite summation formulas.MSC:11C08, 11B39.

On the computing of the generalized order-k Pell numbers in log time

In this paper, we consider the generalized order-k Pell numbers and present an algorithm for computing the sums of the generalized order-k Pell numbers, as well as the Pell numbers themselves. The theoretical basis of using a matrix method for deriving the algorithm is also discussed.