Journal of Integer Sequences, Vol. 23 (2020), Article 20.3.6

On Generalized Delannoy Numbers

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


The Delannoy numbers and the figurate numbers for n-dimensional cross polytopes are doubly-recursive sequences that satisfy the same recursion, and indeed have similar formulae, differing by one parameter. Further varying that parameter, we discover an infinite collection of doubly recursive sequences that satisfy the same recursion. These sequences enumerate certain types of lattice paths using the steps (1, 0), (0, 1), and (1,1) and certain types of words on three letters. We use these combinatorial interpretations to prove relationships among the sequences.

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

Received October 30 2019; revised version received March 16 2020. Published in Journal of Integer Sequences, March 17 2020.

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