Journal of Integer Sequences, Vol. 27 (2024), Article 24.1.8

Delannoy Constructions

Steven Edwards and William Griffiths
Department of Mathematics
Kennesaw State University
Marietta, GA 30060


The Delannoy numbers satisfy a recurrence in two variables and have been used to count lattice paths. We examine related arrays, the generalized Delannoy numbers. We extend properties of the Delannoy numbers to these arrays using combinatorial methods associating these numbers with lattice paths. We generalize these results to any array that satisfies the Delannoy recurrence.

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(Concerned with sequences A002415 A005893 A008288 A034827 A051890 A058331 A093328 A097080 A142978.)

Received May 24 2023; revised version received November 27 2023. Published in Journal of Integer Sequences, January 14 2024.

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