High Quality Content by WIKIPEDIA articles! In mathematics, a Schroder number describes the number of paths from the southwest corner (0, 0) of an n x n grid to the northeast corner (n, n), using only single steps north, northeast, or east, that do not rise above the SW–NE diagonal. Similarly, the Schroder numbers count the number of ways to divide a rectangle into n + 1 smaller rectangles using n cuts; with the restriction that there are n points inside the rectangle, no two of these points falling on the same line parallel to either the x-axis or y-axis, and each cut intersects one of the points and divides only a single rectangle in two.

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