Geodesic
Objects counted by the central Delannoy numbers
Journal of integer sequences, Tome 6 (2003) no. 1
The central Delannoy numbers, d_n_n >=0 = 1,3,13,63,321, 1683, 8989, 48639,$ \dots $(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.
Classification : 05A15
Keywords: delannoy numbers, lattice paths, narayana numbers, schr$\ddot $oder numbers 
@article{JIS_2003__6_1_a1,
     author = {Sulanke,  Robert A.},
     title = {Objects counted by the central {Delannoy} numbers},
     journal = {Journal of integer sequences},
     year = {2003},
     volume = {6},
     number = {1},
     zbl = {1012.05008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2003__6_1_a1/}
}
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Sulanke,  Robert A. Objects counted by the central Delannoy numbers. Journal of integer sequences, Tome 6 (2003) no. 1. http://geodesic.mathdoc.fr/item/JIS_2003__6_1_a1/