Geodesic
Equivalence classes of Motzkin paths modulo a pattern of length at most two
Journal of integer sequences, Tome 18 (2015) no. 7
For any pattern $\alpha $ of length at most two, we enumerate equivalence classes of Motzkin paths where two paths of the same length are equivalent whenever they coincide on all occurrences of the pattern $\alpha $.
Classification : 68R15
Keywords: Motzkin path, equivalence relation, statistics 
@article{JIS_2015__18_7_a0,
     author = {Baril,  Jean-Luc and Petrossian,  Armen},
     title = {Equivalence classes of {Motzkin} paths modulo a pattern of length at most two},
     journal = {Journal of integer sequences},
     year = {2015},
     volume = {18},
     number = {7},
     zbl = {1337.68216},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2015__18_7_a0/}
}
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Baril,  Jean-Luc; Petrossian,  Armen. Equivalence classes of Motzkin paths modulo a pattern of length at most two. Journal of integer sequences, Tome 18 (2015) no. 7. http://geodesic.mathdoc.fr/item/JIS_2015__18_7_a0/