cp's OEIS Frontend

A350718 Number of regions in a regular n-gon with all diagonals drawn whose edges all have a different number of facing edges.

%I A350718 #16 Feb 04 2022 22:36:40
%S A350718 0,0,0,0,0,0,0,0,44,0,130,84,180,128,374,180,418,440,714,704,1104,624,
%T A350718 1750,1976,2484,2744,3190,2880,3658,4416,5280,6188,7000,7128,8214,
%U A350718 8892,10296,10560,13120,14028,16082,15928,22140,20332,22466,26112,27538,29200,36924,36504,35934,40284,41140
%N A350718 Number of regions in a regular n-gon with all diagonals drawn whose edges all have a different number of facing edges.
%C A350718 See A351045 for details of an edge's count of facing edges in an n-gon with all diagonals drawn.
%C A350718 For n = 3 to n = 80 the regions with edges all with a different number of facing edges are all triangles or quadrilaterals. The 81-gon is the first n-gon to contain pentagons with this property. The largest number of edges possible for such regions is unknown.
%H A350718 Scott R. Shannon, <a href="/A350718/b350718.txt">Table of n, a(n) for n = 3..140</a>
%H A350718 Scott R. Shannon, <a href="/A350718/a350718.gif">Image for n = 11</a>. This is the first n-gon to contain regions whose edges all have a different facing edge count. In this and other images such regions are highlighted in gray.
%H A350718 Scott R. Shannon, <a href="/A350718/a350718_1.gif">Image for n = 13</a>.
%H A350718 Scott R. Shannon, <a href="/A350718/a350718_2.gif">Image for n = 18</a>.
%H A350718 Scott R. Shannon, <a href="/A350718/a350718_3.gif">Image for n = 81</a>. This is zoomed-in on one of the pentagons whose edges all have a different facing edge count: 6,7,8,9,10.
%e A350718 a(11) = 44. The 11-gon contains forty-four triangles whose three edges all have a different number of facing edges. This is the first n-gon to contain such regions. See the attached image.
%Y A350718 Cf. A351045, A351129, A135565, A007678, A342222, A349784.
%K A350718 nonn
%O A350718 3,9
%A A350718 _Scott R. Shannon_ and _N. J. A. Sloane_, Feb 03 2022