Delannoy Constructions
Steven Edwards and William Griffiths
Department of Mathematics
Kennesaw State University
Marietta, GA 30060
USA
Abstract:
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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