cp's OEIS Frontend

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

%I A217748 #18 Dec 10 2022 10:46:31
%S A217748 1,4,10,18,28,40,54,70,88,108,130,154,180,208,238,270,304,340,378,418,
%T A217748 460,504,550,598,648,700,754,810,868,928,990,1054,1120,1188,1258,1330,
%U A217748 1404,1480,1558,1638,1720,1804,1890,1978,2068,2160,2254,2350,2448,2548
%N A217748 Number of regions with infinite area in the exterior of a regular n-gon with all diagonals drawn.
%C A217748 For n > 3 same as A028552(n-3).
%F A217748 a(n) = n*(n-3) for n > 3.
%F A217748 a(n) = A217745(n) - A217746(n).
%F A217748 From _Amiram Eldar_, Dec 10 2022: (Start)
%F A217748 Sum_{n>=3} 1/a(n) = 29/18.
%F A217748 Sum_{n>=3} (-1)^(n+1)/a(n) = 23/18 - 2*log(2)/3. (End)
%e A217748 a(3) = 1 since the equilateral triangle has no diagonals and therefore one exterior region with infinite area.
%e A217748 a(4) = 4 since the two diagonals of the square divide the exterior in four regions with infinite area.
%e A217748 a(5) = 10 since the ten diagonals of the regular pentagon divide the exterior in ten regions with infinite area of two different shapes.
%t A217748 a[n_] := n*(n - 3); a[3] = 1; Array[a, 50, 3] (* _Amiram Eldar_, Dec 10 2022 *)
%o A217748 (PARI) a(n) = if(n == 3, 1, n*(n-3)); \\ _Amiram Eldar_, Dec 10 2022
%Y A217748 Cf. A004526, A007678, A028552, A164004, A217745, A217746.
%K A217748 nonn
%O A217748 3,2
%A A217748 _Martin Renner_, Mar 23 2013