%I #9 Jan 06 2024 23:59:04

%S 0,0,1,12,0,0,1,40,8,8,0,0,1,100,40,20,10,0,0,0,1,204,132,12,12,0,0,0,

%T 0,0,1,378,280,126,28,0,0,0,0,0,0,0,1,688,528,176,96,0,0,0,0,0,0,0,0,

%U 0,1,1188,864,72,54,36,0,0,0,0,0,0,0,0,0,0,1

%N Irregular table read by rows: T(n,k) is the number of k-gons, k>=3, in a regular 2n-gon when all vertices are connect by straight lines except for the n lines joining diametrically opposite vertices.

%C See A368813 and A368814 for other images of the 2n-gons.

%H Scott R. Shannon, <a href="/A368816/a368816.png">Image for T(7,k)</a>.

%H Scott R. Shannon, <a href="/A368816/a368816.txt">Table for n = 1..100</a>.

%F Sum of row n = A368813(n).

%e The table begins:

%e 0;

%e 0, 1;

%e 12, 0, 0, 1;

%e 40, 8, 8, 0, 0, 1;

%e 100, 40, 20, 10, 0, 0, 0, 1;

%e 204, 132, 12, 12, 0, 0, 0, 0, 0, 1;

%e 378, 280, 126, 28, 0, 0, 0, 0, 0, 0, 0, 1;

%e 688, 528, 176, 96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;

%e 1188, 864, 72, 54, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;

%e 1840, 1360, 620, 220, 20, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;

%e 2508, 2552, 880, 198, 44, 66, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;

%e 3648, 3576, 864, 216, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;

%e .

%e .

%Y Cf. A368813 (regions), A368814 (vertices), A368815 (edges), A368755, A368758.

%K nonn,tabf

%O 1,4

%A _Scott R. Shannon_, Jan 06 2024