On the Bicomplex $k$-Fibonacci Quaternions

Fibonacci Sequences of Quaternions

In this paper Fibonacci sequences of quaternions are introduced, generalizing Fibonacci sequences over commutative rings, and properties of such sequences are investigated. In particular we are concerned with two kinds of Fibonacci sequences of generalized quaternions over finite fields Fp, with p an odd prime, and their periods.

On the complex k-Fibonacci numbers

Abstract: We first study the relationship between the k-Fibonacci numbers and the elements of a subset of Q. Later, and since generally studies that are made on the Fibonacci sequences consider that these numbers are integers, in this article, we study the possibility that the index of the k-Fibonacci number is fractional; concretely, 2n+1 2 . In this way, the k-Fibonacci numbers that we obtain...

On the Properties of k-Fibonacci Numbers

On the properties of k-Fibonacci and k-Lucas numbers

In this paper, some properties of k−Fibonacci and k−Lucas numbers are derived and proved by using matrices S = k 2 1 2 k 2+4 2 k 2 and M = 

On k-Fibonacci numbers of arithmetic indexes

In this paper, we study the sums of k-Fibonacci numbers with indexes in an arithmetic sequence, say anþ r for fixed integers a and r. This enables us to give in a straightforward way several formulas for the sums of such numbers. 2008 Elsevier Inc. All rights reserved.