Mathematical analysis reveals Binet's formula and generating functions for tri-periodic number sequences, suggesting new insights.
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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Yılmaz et al. (2025) studied this question.
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