On Certain Power Horadam Sequences

Abstract

In this study, firstly, we analyzed power Fibonacci sequences defined by Ide and Renault in [13]. Then, we described two power Horadam sequences modulo s for u=1,v=3 and u=3,v=1, respectively. We determined those modulus s for which the two power Horadam sequences exist and the number of such sequences for a given s. We formulated the periods of these power Horadam sequences in terms of the periods of Horadam sequences for u=1,v=3 and u=3,v=1. Finally, we compared that the period formulas of power Horadam sequences which we obtained and the period formulas of power Fibonacci sequences. We found that, the periods formulas of the power Horadam sequences for u=3,v=1 are the same as the period formulas of the power Fibonacci sequences; but for u=1,v=3, a certain relationship couldn’t be established between the periods of these power sequences.

Keywords

• horadam sequence
• power fibonacci sequence
• period
• horadam dizisi
• fibonacci kuvvet dizisi
• periyot