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We study nearest-neighbors walks on the two-dimensional square lattice, that is, models of walks on Z^2 defined by a fixed step set that is a subset of the non-zero vectors with coordinates 0, 1 or -1. We concern ourselves with the enumeration of such walks starting at the origin and constrained to remain in the quarter plane N^2, counted by their length and by the position of their ending point. Bousquet-Mélou and Mishna [Contemp. Math., pp. 1--39, Amer. Math. Soc., 2010] identified 19 modelsarXiv:1606.02982v3 fatcat:qf4dqhlyizfavpspc3r5z2ys24