August 11, 2025Open Access

Tri–Periodic Fibonacci Numbers and Tri–Periodic Leonardo Numbers

Key Points

Binet's formula provides a closed-form expression for the tri-periodic fibonacci numbers, enhancing computational analysis.
The study establishes generating functions for tri-periodic fibonacci and tri-periodic leonardo numbers, enabling easier manipulation of these sequences.
Cassani's identity highlights a significant relationship within the tri-periodic fibonacci sequence, broadening its mathematical implications.
This research contributes to the broader field of number theory, emphasizing the unique properties of tri-periodic sequences.

Abstract

In this study, we explore the properties of tri-periodic Fibonacci and tri-periodic Leonardo number sequences. Then we derive generating function of these sequences and give Binet's formula for the tri-periodic Fibonacci sequence. Furthermore, we present Cassani's identity associated with tri-periodic Fibonacci sequnce.

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Cite This Study

Yılmaz et al. (Tue,) studied this question.

synapsesocial.com/papers/68a360d60a429f797332903e https://doi.org/https://doi.org/10.20944/preprints202507.0739.v2