%I #18 Mar 12 2016 22:57:26
%S 3,29,299,2177,10482,41348
%N The number of spheres on which the points defined by A222268 lie.
%C Given a cubic n X n X n grid of points, a collection of lines is produced by constructing a line through every pair of points. A222267 gives the count of such lines. A collection of points is produced by taking the points of intersection of those lines. A222268 gives the count of such points. Each point in such a collection will lie on a particular sphere centred at the center of the cubic grid. a(n) is the total number of such spheres, including the radius-zero sphere.
%e A 2 X 2 X 2 grid of points defines 28 distinct lines which intersect in a total of 15 points (including the original 8 points). One of these points is the center of the grid, 8 of them are the vertices of the cube and 6 are the face-centers of the cube. So, a(2) = 3.
%Y Cf. A222267, A222268.
%K nonn,more
%O 2,1
%A _Clive Tooth_, Feb 28 2016