Journal of Integer Sequences, Vol. 6 (2003), Article 03.1.5

Objects Counted by the Central Delannoy Numbers

Robert A. Sulanke
Department of Mathematics
Boise State University
Boise, Idaho 83725
USA

Abstract: The central Delannoy numbers, d_n_{n >=0} = 1,3,13,63,321, 1683, 8989, 48639, ... (A001850 of {\it The On-Line Encyclopedia of Integer Sequences}) will be defined so that d_n counts the lattice paths running from (0,0) to (n,n) that use the steps (1,0), (0,1), and (1,1). In a recreational spirit we give a collection of 29 configurations that these numbers count.

(Concerned with sequence A001850 .)

Received November 13, 2002; revised version received February 12, 2003. Published in Journal of Integer Sequences March 2, 2003.