A217754 Number of different kinds of polygonal regions with finite area in the exterior of a regular n-gon with all diagonals drawn.
0, 0, 0, 0, 1, 1, 2, 2, 4, 3, 4, 4, 4, 4, 5
Offset: 3
Examples
a(7) = 1 since the 35 exterior regions of the regular heptagon built by all diagonals consist of one kind of polygon (with finite area), i.e., 1 triangle (7 times), and three different regions with infinite area (two 7 times, one 14 times). a(8) = 1 since the 64 exterior regions of the regular octagon built by all diagonals consist of one kind of polygon (with finite area), i.e., 2 triangles (one 8 times, one 16 times), and three different regions with infinite area (one 8 times, two 16 times). a(9) = 2 since the 117 exterior regions of the regular 9-gon (nonagon) built by all diagonals consist of two different kinds of polygons (with finite area), i.e., 3 triangles (one 9 times, two 18 times) and 2 quadrilaterals (each 9 times), and four different regions with infinite area (two 9 times, two 18 times).