Geodesic
Animals and 2-Motzkin paths
Journal of integer sequences, Tome 8 (2005) no. 5
We consider an animal $S$ as a set of points in the coordinate plane that are reachable from the origin (0,0) through points in $S$ by steps from (1,0),(0,1),(1,1),(-1,-1). In this paper, we give a combinatorial bijection with 2-Motzkin paths, i.e., the Motzkin paths with two different horizontal steps.
Classification : 05A15
Keywords: animals, directed animals, Motzkin paths, Catalan paths, binomial coefficients 
@article{JIS_2005__8_5_a6,
     author = {Woan,  Wen-jin},
     title = {Animals and {2-Motzkin} paths},
     journal = {Journal of integer sequences},
     year = {2005},
     volume = {8},
     number = {5},
     zbl = {1103.05008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2005__8_5_a6/}
}
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Woan,  Wen-jin. Animals and 2-Motzkin paths. Journal of integer sequences, Tome 8 (2005) no. 5. http://geodesic.mathdoc.fr/item/JIS_2005__8_5_a6/