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A358951 Irregular table read by rows: T(n,k) = number of k-gons, k >= 3, formed inside a triangle 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).

%I A358951 #10 Dec 19 2022 13:32:13
%S A358951 1,12,180,42,6,810,576,72,6,6786,4932,744,48,6,13662,12522,2568,258,
%T A358951 12,72582,64932,14376,1632,36,6,164484,155088,38688,5958,414,18,
%U A358951 439524,422370,114804,18462,1392,120,750108,749928,211518,35226,3336,204,6,2265462,2240994,647184,109602,10230,666,18
%N A358951 Irregular table read by rows: T(n,k) = number of k-gons, k >= 3, formed inside a triangle 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 A358951 The number of points along each edge is given by A005728(n).
%H A358951 Scott R. Shannon, <a href="/A358951/a358951.jpg">Image for n = 7</a>.
%H A358951 Wikipedia, <a href="https://en.wikipedia.org/wiki/Farey_sequence">Farey sequence</a>.
%F A358951 Sum of row n = A358948(n).
%e A358951 The table begins:
%e A358951 1;
%e A358951 12;
%e A358951 180, 42, 6;
%e A358951 810, 576, 72, 6;
%e A358951 6786, 4932, 744, 48, 6;
%e A358951 13662, 12522, 2568, 258, 12;
%e A358951 72582, 64932, 14376, 1632, 36, 6;
%e A358951 164484, 155088, 38688, 5958, 414, 18;
%e A358951 439524, 422370, 114804, 18462, 1392, 120;
%e A358951 750108, 749928, 211518, 35226, 3336, 204, 6;
%e A358951 2265462, 2240994, 647184, 109602, 10230, 666, 18;
%e A358951 3263436, 3312270, 990072, 176172, 18294, 1188, 66;
%e A358951 .
%e A358951 .
%Y A358951 Cf. A358948 (regions), A358949 (vertices), A358950 (edges), A358889, A006842, A006843, A005728, A358882.
%K A358951 nonn,tabf
%O A358951 1,2
%A A358951 _Scott R. Shannon_ and _N. J. A. Sloane_, Dec 07 2022