
EXAMPLE

a(7) = 7 since the 28 diagonals of the regular heptagon divide the exterior in 35 regions consisting of seven triangles (with finite area), i.e., 1 triangle (7 times), and 28 regions with infinite area of three different shapes (two 7 times, one 14 times).
a(8) = 24 since the 40 diagonals of the regular octagon divide the exterior in 64 regions consisting of 24 polygons (with finite area), i.e., 2 triangles (one 8 times, one 16 times), and 40 regions with infinite area of three different shapes (one 8 times, two 16 times).
a(9) = 63 since the 54 diagonals of the regular 9gon (nonagon) divide the exterior in 117 regions consisting of 63 polygons (with finite area), i.e., 3 triangles (one 9 times, two 18 times) and 2 quadrilaterals (each 9 times), and 54 regions with infinite area of four different shapes (two 9 times, two 18 times).
