Halving lines (Neil Sloane)

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Given n, find a subset S of R^2 of order 2n, such that |{(p1,p2) in S, the line p1-p2 divides S into 2 sets of equal size}| is as big as possible A076523: 1,3,6,9,13,18,22 Maximal number of halving lines for 2n points in plane. Let S be a set of n points in the plane. A halving line is a line through two points in S that splits the remaining points into two equal-sized sets Please send us a simpler description.