A358889 - OEIS

%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