Table of n, a(n) for n=2..10.
The 20 planes defined by the points of the 2 X 2 X 2 grid fall into 13 families of parallel planes: 3 parallel to the faces, 4 perpendicular to the space diagonals and 6 which are the planes defined by an edge and its opposite edge. So a(2)=13.
Cf. A222267, A270578.
Sequence in context: A065411 A354466 A038492 * A297223 A199023 A152585
Adjacent sequences: A270576 A270577 A270578 * A270580 A270581 A270582
Clive Tooth, Mar 19 2016