cp's OEIS Frontend

A355801 Irregular table read by rows: T(n,k) is the number of k-sided polygons, for k>=3, in a square when straight line segments connect the n-1 points between each corner that divide each edge into n equal parts to the n-1 points on the edge on the opposite side of the square.

%I A355801 #17 Jan 04 2024 14:29:31
%S A355801 0,1,0,4,12,12,56,32,16,156,124,24,8,0,4,384,228,72,28,716,648,144,68,
%T A355801 8,4,1312,1144,240,112,8,2244,1912,528,256,3528,3072,696,360,16,5012,
%U A355801 5536,1296,524,48,28,7696,6596,1960,572,16,10340,11448,2968,1028,160,24,14520,14428,3872,1156,104,8
%N A355801 Irregular table read by rows: T(n,k) is the number of k-sided polygons, for k>=3, in a square when straight line segments connect the n-1 points between each corner that divide each edge into n equal parts to the n-1 points on the edge on the opposite side of the square.
%C A355801 Up to n = 50 the maximum sided k-gon created is the 8-gon. It is plausible this is the maximum sided k-gon for all n, although this is unknown.
%C A355801 See A355798 for more images of the square.
%C A355801 The keyword "look" is for the n = 10 image. - _N. J. A. Sloane_, Jul 21 2022
%H A355801 Scott R. Shannon, <a href="/A355801/a355801.jpg">Image for n = 10</a>.
%e A355801 The table begins:
%e A355801 0,     1;
%e A355801 0,     4;
%e A355801 12,    12;
%e A355801 56,    32,    16;
%e A355801 156,   124,   24,   8,    0,   4;
%e A355801 384,   228,   72,   28;
%e A355801 716,   648,   144,  68,   8,   4;
%e A355801 1312,  1144,  240,  112,  8;
%e A355801 2244,  1912,  528,  256;
%e A355801 3528,  3072,  696,  360,  16;
%e A355801 5012,  5536,  1296, 524,  48,  28;
%e A355801 7696,  6596,  1960, 572,  16;
%e A355801 10340, 11448, 2968, 1028, 160, 24;
%e A355801 14520, 14428, 3872, 1156, 104, 8;
%e A355801 19588, 19156, 5296, 2052, 160, 8;
%e A355801 25392, 26112, 7160, 2152, 208, 24;
%e A355801 31820, 37244, 9936, 3240, 488, 64;
%e A355801 .
%e A355801 .
%Y A355801 Cf. A355798 (regions), A355799 (vertices), A355800 (edges), A355801 (k-gons), A255011 (all vertices), A290131, A331452, A335678.
%K A355801 nonn,tabf,look
%O A355801 1,4
%A A355801 _Scott R. Shannon_, Jul 17 2022