The diagram below shows a [unparseable or potentially dangerous latex formula] by [unparseable or potentially dangerous latex formula] rectangular array of points, each of which is 1 unit away from its nearest neighbors.
Define a [unparseable or potentially dangerous latex formula] to be a sequence of distinct points of the array with the property that the distance between consecutive points of the sequence is strictly increasing. Let [unparseable or potentially dangerous latex formula] be the maximum possible number of points in a growing path, and let [unparseable or potentially dangerous latex formula] be the number of growing paths consisting of exactly [unparseable or potentially dangerous latex formula] points. Find [unparseable or potentially dangerous latex formula]
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