Some higher-order identities for generalized bi-periodic Horadam sequences

Leung H., TAN E.

TURKISH JOURNAL OF MATHEMATICS, vol.44, no.5, pp.1687-1700, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 44 Issue: 5
  • Publication Date: 2020
  • Doi Number: 10.3906/mat-1905-62
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1687-1700
  • Keywords: Horadam sequence, generalized Fibonacci sequence, generalized Lucas sequence, congruence, FIBONACCI
  • Ankara University Affiliated: Yes

Abstract

In this paper, we derive higher-order identities for the generalized bi-periodic Horadam sequences. Some of our results generalize the identities for the classical Fibonacci sequences and Horadam sequences obtained by Hoggatt, Horadam and Waddill. As an application, we derive some congruence properties satisfied by the generalized bi-periodic Horadam sequences.