In this paper, firstly, we introduce the Ql-Generating matrix for the bi-periodic Lucas numbers. Then, by taking into account this matrix representation, we obtain some properties for the bi-periodic Fibonacci and Lucas numbers.

In this study, we define a generalization of Lucas sequence {pn}. Then we obtain Binet formula of sequence {pn} . Also, we investigate relationships between generalized Fibonacci and Lucas sequences.

We obtain some new formulas for the Fibonacci and Lucas p-numbers, by using the symmetric infinite matrix method. We also give some results for the Fibonacci and Lucas p-numbers by means of the binomial inverse pairing.

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. 2003 Elsevier Inc. All rights reserved.

In this paper we consider the generalized order-k Fibonacci and Lucas numbers. We give the generalized Binet formula, combinatorial representation and some relations involving the generalized order-k Fibonacci and Lucas numbers.

If f is a binary word and d a positive integer, then the generalized Fibonacci cube Qd(f) is the graph obtained from the d-cube Qd by removing all the vertices that contain f as a factor, while the generalized Lucas cube Qd( ↽Ð f ) is the graph obtained from Qd by removing all the vertices that have a circulation containing f as a factor. The Fibonacci cube Γd and the Lucas cube Λd are the grap...

The aim of this paper is to give new results about factorizations of the Fibonacci numbers Fn and the Lucas numbers Ln. These numbers are defined by the second order recurrence relation an+2 = an+1+an with the initial terms F0 = 0, F1 = 1 and L0 = 2, L1 = 1, respectively. Proofs of theorems are done with the help of connections between determinants of tridiagonal matrices and the Fibonacci and ...