Catalan transform of the k-Pell, k-Pell-Lucas and modified k-Pell sequence


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Tastan M., Özkan E.

NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS, cilt.27, sa.1, ss.198-207, 2021 (Hakemli Dergi) identifier

Özet

In this study, we present the Catalan transforms of the k-Pell sequence, the k-Pell-Lucas sequence and the Modified k-Pell sequence and examine the properties of the sequences. Then we apply the Hankel transform to the Catalan transforms of the k-Pell sequence, the Catalan transform of the k-Pell-Lucas sequence and the Catalan transform of the Modified k-Pell sequence. Also, we obtain the generating functions of the Catalan transform of the k-Pell sequence, k-Pell-Lucas sequence and Modified k-Pell sequence. Furthermore, we acquire an interesting characteristic related to the determinant of the Hankel transform of the sequences.