A128153 The number of regular pentagons found by constructing points on each side of the pentagon 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 pentagon 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 pentagon. Also connect all vertices of the pentagon with lines that are parallel to at least 1 side of the pentagon. With 0 points, there is only 1 pentagon. With 1 point (a midpoint on each side), 9 regular pentagons are found. With 2 points, 20 regular pentagons are found in total.

1, 9, 20, 37