On Certain Fourth-Order Linear Recursive Sequences

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

Symmetry, cilt.17, sa.1, 2025 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 17 Sayı: 1
  • Basım Tarihi: 2025
  • Doi Numarası: 10.3390/sym17010041
  • Dergi Adı: Symmetry
  • Derginin Tarandığı İndeksler: 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
  • Anahtar Kelimeler: Binet formula, Diophantine equation, recurrence relation, subbalancing numbers
  • İstanbul Üniversitesi Adresli: Evet

Özet

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.