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%I #19 Dec 06 2022 19:33:37
%S 4,48,8,712,304,24,3368,2400,280,16,27424,20360,4784,504,32,56000,
%T 47088,10912,1400,88,8,292424,255608,69368,11504,960,56,658800,590208,
%U 175856,30160,2496,200,24,1748112,1593912,506496,93584,9616,520,24,2981448,2778456,890368,166912,17192,1144,48
%N Table read by rows: T(n,k) = number of k-gons, k >= 3, formed inside a square with edge length 1 by the straight line segments mutually connecting all vertices and points that divide the sides into segments with lengths equal to the Farey series of order n = A006842(n,m)/A006843(n,m), m = 1..A005728(n).
%C The number of points along each edge is given by A005728(n).
%H Scott R. Shannon, <a href="/A358889/a358889.jpg">Image for n = 5</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Farey_sequence">Farey sequence</a>.
%F Sum of row n = A358886(n).
%e The table begins:
%e 4;
%e 48, 8;
%e 712, 304, 24;
%e 3368, 2400, 280, 16;
%e 27424, 20360, 4784, 504, 32;
%e 56000, 47088, 10912, 1400, 88, 8;
%e 292424, 255608, 69368, 11504, 960, 56;
%e 658800, 590208, 175856, 30160, 2496, 200, 24;
%e 1748112, 1593912, 506496, 93584, 9616, 520, 24;
%e 2981448, 2778456, 890368, 166912, 17192, 1144, 48;
%e .
%e .
%Y Cf. A358886 (regions), A358887 (vertices), A358888 (edges), A006842, A006843, A005728, A358885.
%Y The Farey Diagrams Farey(m,n) are studied in A358298-A358307 and A358882-A358885, the Completed Farey Diagrams of order (m,n) in A358886-A358889.
%K nonn,more,tabl
%O 1,1
%A _Scott R. Shannon_ and _N. J. A. Sloane_, Dec 05 2022
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