On the Universal Regularity of the Numbers of Generalized Recurrence Sequence and Solutions to Its Characteristic Equation of Second Order

Abstract

In this work shows that the classical oscillations of the ratio of neighboring members of the Fibonacci sequences are valid for arbitrary directions on the plane of the phase coordinates, approaching, to a maximum, the solutions to the characteristic quadratic equation at a given point. The values of the solutions to the characteristic equation along the satellites are asymptotically close to their integer values of the corresponding root lines.