Counting D-sets

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Chef likes points located at integer coordinates in a space having N dimensions. In particular, he likes sets of such points having diameter exactly equal to D (called D-sets). The diameter of a set of points is the maximum distance between any pair of points in the set. The distance between two points (a1,a2,...,aN) and (b1,b2,...,bN) is max{|a1-b1|, |a2-b2|, ..., |aN-bN|}. Chef would like to

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