Power Narayana Sequences

Abstract

In this paper, firstly, we investigated the periods of power Jacobsthal sequences and formulated the periods of power Jacobsthal sequences, based on the period of Jacobsthal sequence modulo u. Then, we descibed new infinite integer sequences providing the recurrence relation of Narayana sequence that also be power sequence for some modulus u. We investigated those modulus u for which these power sequences exist. And, we formulated the periods of these power sequences for some prime integers p based on the period of Narayana sequence modulo p. Finally, we compared that periodic properties of Narayana, Fibonacci, Jacobsthal sequences and the power sequences of these sequences.