Geodesic
A bijection between 3-Motzkin paths and Schröder paths with no peak at odd
Journal of integer sequences, Tome 12 (2009) no. 3
A new bijection between 3-Motzkin paths and Schröder paths with no peak at odd height is presented, together with numerous consequences involving related combinatorial structures such as 2-Motzkin paths, ordinary Motzkin paths and Dyck paths.
Classification : 05A05, 05A15, 05A19
Keywords: 3-Motzkin paths, schr$\ddot $oder paths, 2-Motzkin paths, Motzkin paths, Dyck paths, fine paths, riordan paths, Catalan numbers 
@article{JIS_2009__12_3_a7,
     author = {Shapiro,  Louis W. and Wang,  Carol J.},
     title = {A bijection between {3-Motzkin} paths and {Schr\"oder} paths with no peak at odd},
     journal = {Journal of integer sequences},
     year = {2009},
     volume = {12},
     number = {3},
     zbl = {1165.05300},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2009__12_3_a7/}
}
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Shapiro,  Louis W.; Wang,  Carol J. A bijection between 3-Motzkin paths and Schröder paths with no peak at odd. Journal of integer sequences, Tome 12 (2009) no. 3. http://geodesic.mathdoc.fr/item/JIS_2009__12_3_a7/