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A368816 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.

%I A368816 #9 Jan 06 2024 23:59:04
%S A368816 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 A368816 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 A368816 0,1,1188,864,72,54,36,0,0,0,0,0,0,0,0,0,0,1
%N A368816 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 A368816 See A368813 and A368814 for other images of the 2n-gons.
%H A368816 Scott R. Shannon, <a href="/A368816/a368816.png">Image for T(7,k)</a>.
%H A368816 Scott R. Shannon, <a href="/A368816/a368816.txt">Table for n = 1..100</a>.
%F A368816 Sum of row n = A368813(n).
%e A368816 The table begins:
%e A368816 0;
%e A368816 0, 1;
%e A368816 12, 0, 0, 1;
%e A368816 40, 8, 8, 0, 0, 1;
%e A368816 100, 40, 20, 10, 0, 0, 0, 1;
%e A368816 204, 132, 12, 12, 0, 0, 0, 0, 0, 1;
%e A368816 378, 280, 126, 28, 0, 0, 0, 0, 0, 0, 0, 1;
%e A368816 688, 528, 176, 96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
%e A368816 1188, 864, 72, 54, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
%e A368816 1840, 1360, 620, 220, 20, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
%e A368816 2508, 2552, 880, 198, 44, 66, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
%e A368816 3648, 3576, 864, 216, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
%e A368816 .
%e A368816 .
%Y A368816 Cf.  A368813 (regions), A368814 (vertices), A368815 (edges), A368755, A368758.
%K A368816 nonn,tabf
%O A368816 1,4
%A A368816 _Scott R. Shannon_, Jan 06 2024