Geodesic
Difference equations and generating functions for some lattice path problems
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 5, pp. 551-559

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An identity for generating functions is proved in this paper. A novel method to compute the number of restricted lattice paths is developed on the basis of this identity. The method employs a difference equation with non-constant coefficients. Dyck paths, Schröder paths, Motzkins path and other paths are computed to illustrate this method.
Keywords: difference equation, generating function, lattice path. 
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     author = {Sreelatha Chandragiri},
     title = {Difference equations and generating functions for some lattice path problems},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {551--559},
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     volume = {12},
     number = {5},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2019_12_5_a2/}
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Sreelatha Chandragiri. Difference equations and generating functions for some lattice path problems. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 5, pp. 551-559. http://geodesic.mathdoc.fr/item/JSFU_2019_12_5_a2/