On the complex k-Fibonacci numbers

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

Restricted Permutations, Fibonacci Numbers, and k-generalized Fibonacci Numbers

In 1985 Simion and Schmidt showed that the number of permutations in Sn which avoid 132, 213, and 123 is equal to the Fibonacci number Fn+1. We use generating function and bijective techniques to give other sets of pattern-avoiding permutations which can be enumerated in terms of Fibonacci or k-generalized 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.