Original scientific paper

On some properties of k-generalized Fibonacci numbers

Halim Özdemir ; Department of Mathematics, Faculty of Science, Sakarya University, Esentepe Campus, Sakarya, Turkey *
Sinan Karakaya ; Department of Mathematics, Faculty of Science, Sakarya University, Esentepe Campus, Sakarya, Turkey

* Corresponding author.

Abstract

Some identities between the positive integer powers of the matrices X satisfying the equation \(X^{k+1}-(r+1)X^k+rI+\sum\limits_{i=1}^{k-1}(r-1)X^i=0\) and the k-generalized Fibonacci numbers are first established, where k is an integer with \(k\geq 2\). Then, two main formulas, one of which is related to the k-generalized Fibonacci sequence, are given.

Keywords

k-generalized Fibonacci numbers; recurrences; polynomials; matrices

Hrčak ID:

321247

URI

https://hrcak.srce.hr/321247

Publication date:

7.10.2024.

Visits: 0 *