On Certain Fourth-Order Linear Recursive Sequences

KARADENİZ GÖZERİ G., Sarı S., Akgül P.

Symmetry, vol.17, no.1, 2025 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 17 Issue: 1
  • Publication Date: 2025
  • Doi Number: 10.3390/sym17010041
  • Journal Name: Symmetry
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: Binet formula, Diophantine equation, recurrence relation, subbalancing numbers
  • Istanbul University Affiliated: Yes

Abstract

In this paper, we introduce a fourth-order linear recursive sequence that is related to the concept of subbalancing numbers. This sequence is constructed by using the third balancing number in the Diophantine equation of subbalancing numbers and is called the sequence of (Formula presented.) -Lucas subbalancing numbers. Motivated by the results for (Formula presented.) -Lucas subbalancing numbers, we obtain several algebraic identities regarding (Formula presented.) -Lucas subbalancing numbers. Furthermore, we derive some algebraic relations between (Formula presented.) -Lucas subbalancing numbers and some other integer sequences.