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,n}nE, a different generalized k - Horadam sequence {qk,n} and an altered generalized k - Horadam sequence {Qk,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.