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

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 $(F_{k,p}(n))_{n\geq0}$ ( F k , p ( n ) ) n ≥ 0 . In this paper, we study the geometry of roots of the characteristic polynomial of this sequence.

Distance Fibonacci Polynomials by Graph Methods

“…Generalizations of numbers or polynomials of the Fibonacci type existing in the literature are mainly concentrated on combinatorial properties using generating functions or the problem of solving the recurrence relation, called a problem of Binet's formula type, see, for example, [5][6][7]. Note that some generalizations we obtain by changing initial terms and preserving the recurrence equation (see [8,9]) or by modification of the recurrence, see, for instance, [10].…”