cp's OEIS Frontend

A359656 Irregular table read by rows: T(n,k) is the number of k-gons, k>=3, formed in a square with edge length 1 by straight line segments when connecting the internal edge points that divide the sides into segments with lengths equal to the Farey series of order n to the equivalent points on the opposite side of the square.

%I A359656 #12 Jan 11 2023 08:47:49
%S A359656 0,1,0,4,56,40,368,300,48,12,3376,3408,960,96,7536,7524,2240,436,8,
%T A359656 42048,45112,13912,2868,168,28,97720,105980,34496,7020,832,52,8,
%U A359656 267240,290456,100560,20576,2688,160,24,461800,509824,174400,36228,4608,324,16,1411272,1594296,569152,126408,16856,1408,104
%N A359656 Irregular table read by rows: T(n,k) is the number of k-gons, k>=3, formed in a square with edge length 1 by straight line segments when connecting the internal edge points that divide the sides into segments with lengths equal to the Farey series of order n to the equivalent points on the opposite side of the square.
%C A359656 The number of points internal to each edge is given by A005728(n) - 2.
%C A359656 See A359653 and A359654 for images of the square.
%e A359656 The table begins:
%e A359656 0, 1;
%e A359656 0, 4;
%e A359656 56, 40;
%e A359656 368, 300, 48, 12;
%e A359656 3376, 3408, 960, 96;
%e A359656 7536, 7524, 2240, 436, 8;
%e A359656 42048, 45112, 13912, 2868, 168, 28;
%e A359656 97720, 105980, 34496, 7020, 832, 52, 8;
%e A359656 267240, 290456, 100560, 20576, 2688, 160, 24;
%e A359656 461800, 509824, 174400, 36228, 4608, 324, 16;
%e A359656 1411272, 1594296, 569152, 126408, 16856, 1408, 104;
%e A359656 2054616, 2300184, 830280, 184664, 24480, 2332, 128, 8;
%e A359656 5296752, 6001228, 2253456, 517564, 72888, 7532, 472, 4;
%e A359656 .
%e A359656 .
%Y A359656 Cf. A359653 (regions), A359654 (vertices), A359655 (edges), A005728, A358889, A358885, A355801, A358951, A006842, A006843.
%K A359656 nonn,tabf
%O A359656 1,4
%A A359656 _Scott R. Shannon_ and _N. J. A. Sloane_, Jan 10 2023