A128828 The number of regular hexagons found by constructing points on each side of the hexagon such that these points divide each side into equally-sized segments (i.e. a midpoint each side or 2 points on each side placed to divide each side into 3 equally-sized segments or so on), do the same construction for every side of the hexagon so that each side is equally divided in the same way. Connect all such points to each other with lines that are parallel to at least 1 side of the hexagon. With 0 points, there is only 1 hexagon. With 1 point (a midpoint on each side), 2 regular hexagons are found. With 3 points on each side, 15 regular hexagons are found in total and so on.

1, 2, 15, 28, 65, 120