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.
Full version: pdf,
(Concerned with sequences
Received October 30 2019; revised version received March 16 2020.
Published in Journal of Integer Sequences,
March 17 2020.
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