Catalan Transform of the $k$-Fibonacci Sequence

Sergio Falcon

doi:10.4134/CKMS.2013.28.4.827

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Commun. Korean Math. Soc. 2013; 28(4): 827-832

Printed October 1, 2013

https://doi.org/10.4134/CKMS.2013.28.4.827

Catalan Transform of the $k$-Fibonacci Sequence

Sergio Falcon

University of Las Palmas de Gran Canaria

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Abstract

In this paper we apply the Catalan transform to the $k$-Fibo\-nacci sequence finding different integer sequences, some of which are indexed in OEIS and others not. After we apply the Hankel transform to the Catalan transform of the $k$-Fibonacci sequence and obtain an unusual property.

Keywords: $k$-Fibonacci numbers, Catalan numbers, Catalan transform, Hankel transform