A NOTE ON NEW GENERALIZATIONS OF k-HORADAM SEQUENCES AND THE POWER SEQUENCES OF THESE GENERALIZATIONS

Çelemoğlu Ç.

JOURNAL OF SCIENCE AND ARTS, no.3, pp.625-638, 2021 (ESCI) identifier

  • Publication Type: Article / Article
  • Publication Date: 2021
  • Doi Number: 10.46939/j.sci.arts-21.3-a03
  • Journal Name: JOURNAL OF SCIENCE AND ARTS
  • Journal Indexes: Emerging Sources Citation Index (ESCI)
  • Page Numbers: pp.625-638
  • Keywords: generalized k - Horadam sequence, generating function, generalized Fibonacci sequence, extended Binet's formula, the power Fibonacci sequence module m, LUCAS-NUMBERS, FIBONACCI
  • Ondokuz Mayıs University Affiliated: Yes

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.