Geodesic
A relation between restricted and unrestricted weighted Motzkin paths
Journal of integer sequences, Tome 9 (2006) no. 1
We consider those lattice paths that use the steps "up", "level", and "down" with assigned weights $w,b,c$. In probability theory, the total weight is 1. In combinatorics, we replace weight by the number of colors. Here we give a combinatorial proof of a relation between restricted and unrestricted weighted Motzkin paths.
Classification : 05A15, 05A19
Keywords: Motzkin paths, combinatorial identity 
@article{JIS_2006__9_1_a0,
     author = {Woan,  Wen-jin},
     title = {A relation between restricted and unrestricted weighted {Motzkin} paths},
     journal = {Journal of integer sequences},
     year = {2006},
     volume = {9},
     number = {1},
     zbl = {1101.05008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2006__9_1_a0/}
}
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Woan,  Wen-jin. A relation between restricted and unrestricted weighted Motzkin paths. Journal of integer sequences, Tome 9 (2006) no. 1. http://geodesic.mathdoc.fr/item/JIS_2006__9_1_a0/