The Schröder number S_n is the number of lattice paths in the Cartesian plane that start at (0, 0), end at (n, n), contain no points above the line y = x, and are composed only of steps (0, 1), (1, 0), and (1, 1), i.e., ->, ↑, and ↗. The diagrams illustrating the paths generating S_1, S_2, and S_3 are illustrated above.
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