On the characteristic polynomial of ( k , p ) $(k,p)$ -Fibonacci sequence

Abstract

Abstract Recently, Bednarz introduced a new two-parameter generalization of the Fibonacci sequence, which is called the ( k , p ) $(k,p)$ -Fibonacci sequence and denoted by ( F k , p ( n ) ) n ≥ 0 $(F_{k,p}(n))_{n\geq0}$ . In this paper, we study the geometry of roots of the characteristic polynomial of this sequence.

Keywords

• Generalized Fibonacci sequence
• Characteristic polynomial
• Eneström–Kakeya theorem
• Descartes’ sign rule