A217746 Number of polygonal regions with finite area in the exterior of a regular n-gon with all diagonals drawn.

0, 0, 0, 0, 7, 24, 63, 120, 242, 384, 650, 896, 1425, 1872, 2703

Offset

3,5

Links

Table of n, a(n) for n=3..17.

Formula

a(n) = A217745(n) - A217748(n)

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 9-gon (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).

Crossrefs

Cf. A007678, A217745, A217748.

Sequence in context: A029585 A114291 A211382 * A211381 A339254 A305676

Adjacent sequences: A217743 A217744 A217745 * A217747 A217748 A217749

Keyword

nonn

Author

Martin Renner, Mar 23 2013

Status

approved