Abstract: The Gessel number P(n, r) represents the number of lattice paths in a plane with unit horizontal and vertical steps from (0, 0) to (n + r, n + r - 1) that never touch any of the points from the set . In this paper, we use combinatorial arguments to derive a recurrence relation between P(n, r) and Also, we give a new proof for a well-known closed formula for P(n, r). Moreover, a new combinatorial interpretation for the Gessel numbers is presented.
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Keywords and phrases: Gessel numbers, Catalan numbers, central binomial coefficient, lattice paths
Received: December 15, 2023; Accepted: March 11, 2024; Published: April 1, 2024
How to cite this article: Jovan Mikić, A note on the Gessel numbers, JP Journal of Algebra, Number Theory and Applications 63(3) (2024), 225-235. http://dx.doi.org/10.17654/0972555524013
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
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