Journal of Integer Sequences, Vol. 25 (2022), Article 22.4.6

On The Complex-Type Catalan Transform of the k-Fibonacci Numbers

Ömür Deveci
Department of Mathematics
Faculty of Science and Letters
Kafkas University
36100, Turkey

Anthony G. Shannon
Honorary Fellows
Warrane College
University of New South Wales
2033, Australia


We define a type of complex Catalan number and find some its properties. We also produce a complex Catalan transform and its inverse, together with associated generating functions and related matrices. These lead to connections with complex Catalan transforms of the k-Fibonacci numbers and the determinants of their Hankel matrices. The paper finishes with a conjecture.

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(Concerned with sequences A000108.)

Received February 21 2022; revised versions received March 10 2022; April 4 2022. Published in Journal of Integer Sequences, April 11 2022.

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