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

Year 2024, Volume: 42 Issue: 5, 1439 - 1447, 04.10.2024

İbrahim Gökcan , Ali Hikmet Değer , Ümmügülsün Çağlayan

Abstract

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 Fibo-nacci 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.

Keywords

Continued Fraction, Generalized Fibonacci Numbers, Modular Group

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