Geodesic
A note on the enumeration of diffusion walks in the first octant by their number of contacts with the diagonal
Journal of integer sequences, Tome 8 (2005) no. 4
Diffusion walks take steps in the four directions N, E, S, and W. We derive a closed form for the number of diffusion walks from the origin to some point $(n,n)$ on the diagonal in $k$ steps inside the first octant, touching the diagonal exactly $c$ times.
Classification : 05A05, 05A15
Keywords: random walks, diffusion, contacts, adsorption 
@article{JIS_2005__8_4_a6,
     author = {Niederhausen,  Heinrich},
     title = {A note on the enumeration of diffusion walks in the first octant by their number of contacts with the diagonal},
     journal = {Journal of integer sequences},
     year = {2005},
     volume = {8},
     number = {4},
     zbl = {1102.60042},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2005__8_4_a6/}
}
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Niederhausen,  Heinrich. A note on the enumeration of diffusion walks in the first octant by their number of contacts with the diagonal. Journal of integer sequences, Tome 8 (2005) no. 4. http://geodesic.mathdoc.fr/item/JIS_2005__8_4_a6/