Some approximations and identities from special sequences for the vertices of suborbital graphs

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GÖKCAN İ., DEĞER A. H., ÇAĞLAYAN Ü.

SIGMA JOURNAL OF ENGINEERING AND NATURAL SCIENCES-SIGMA MUHENDISLIK VE FEN BILIMLERI DERGISI, cilt.42, sa.5, ss.1439-1447, 2024 (ESCI, Scopus)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 42 Sayı: 5
• Basım Tarihi: 2024
• Doi Numarası: 10.14744/sigma.2024.00112112
• Dergi Adı: SIGMA JOURNAL OF ENGINEERING AND NATURAL SCIENCES-SIGMA MUHENDISLIK VE FEN BILIMLERI DERGISI
• Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
• Sayfa Sayıları: ss.1439-1447
• Karadeniz Teknik Üniversitesi Adresli: Evet

Özet

In this study, we investigate the vertices arising from the action of a suborbital graph, in terms of continued fractions, matrix, and recurrence relations. Using the approximation of Fibonacci sequence by the Binet formula, we demonstrate that the vertices of the suborbital graph are related to Lucas numbers. Then, we provide new identities and approximations regarding Fibonacci, Lucas, Pell, and Pell-Lucas numbers.