A217748 Number of regions with infinite area in the exterior of a regular n-gon with all diagonals drawn.

1, 4, 10, 18, 28, 40, 54, 70, 88, 108, 130, 154, 180, 208, 238, 270, 304, 340, 378, 418, 460, 504, 550, 598, 648, 700, 754, 810, 868, 928, 990, 1054, 1120, 1188, 1258, 1330, 1404, 1480, 1558, 1638, 1720, 1804, 1890, 1978, 2068, 2160, 2254, 2350, 2448, 2548

Offset: 3

Author

Martin Renner, Mar 23 2013

Keywords

• nonn

Comments

For n > 3 same as A028552(n-3).

Examples

			a(3) = 1 since the equilateral triangle has no diagonals and therefore one exterior region with infinite area.
a(4) = 4 since the two diagonals of the square divide the exterior in four regions with infinite area.
a(5) = 10 since the ten diagonals of the regular pentagon divide the exterior in ten regions with infinite area of two different shapes.
		

Crossrefs

Cf. A004526, A007678, A028552, A164004, A217745, A217746.

Programs

Mathematica

a[n_] := n*(n - 3); a[3] = 1; Array[a, 50, 3] (* Amiram Eldar, Dec 10 2022 *)

PARI

a(n) = if(n == 3, 1, n*(n-3)); \\ Amiram Eldar, Dec 10 2022

Formula

a(n) = n*(n-3) for n > 3.

a(n) = A217745(n) - A217746(n).

From Amiram Eldar, Dec 10 2022: (Start)

Sum_{n>=3} 1/a(n) = 29/18.

Sum_{n>=3} (-1)^(n+1)/a(n) = 23/18 - 2*log(2)/3. (End)