A Note on New Generalizations of K-Horadam Sequences and the Power Sequences of These Generalizations

Abstract

In this article, firstly, we have described new generalizations of generalized k - Horadam sequence and we named the generalizations as another generalized k - Horadam sequence {H-k,H-n'}(n is an element of N), a different generalized k - Horadam sequence {q(k,n)} and an altered generalized k - Horadam sequence {Q(k,n)}, respectively. Then, we have studied properties of these new generalizations and we have obtained generating function and extended Binet formula for each generalization. Also, we have introduced a power sequence for an altered generalized k - Horadam sequence in order to be used in different applications like number theory, cryptography, coding theory and engineering.