cp's OEIS Frontend

A355841 Irregular table read by rows: T(n,k) is the number of k-sided polygons formed, for k>=3, in a square when straight line segments connect the n+1 points along each edge that divide it into n equal parts to the n+1 points on the edge on the opposite side of the square.

%I A355841 #13 Jan 04 2024 14:13:03
%S A355841 4,40,128,44,12,320,152,24,616,512,84,28,1240,744,120,40,1936,1928,
%T A355841 372,136,8,3288,2656,616,160,4960,4500,1020,332,48,7224,6472,1424,392,
%U A355841 16,9760,11064,2564,824,72,16,14144,12424,2696,856,32,18312,20604,5308,1468,328,16,24384,25392,5968,1584,160,8
%N A355841 Irregular table read by rows: T(n,k) is the number of k-sided polygons formed, for k>=3, in a square when straight line segments connect the n+1 points along each edge that divide it into n equal parts to the n+1 points on the edge on the opposite side of the square.
%C A355841 This sequence is similar to A355801 but here the corner vertices of the square are also connected to points on the opposite edge.
%C A355841 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 A355841 See A355838 for more images of the square.
%H A355841 Scott R. Shannon, <a href="/A355841/a355841.jpg">Image for n = 10</a>.
%e A355841 The table begins:
%e A355841 4;
%e A355841 40;
%e A355841 128,   44,    12;
%e A355841 320,   152,   24;
%e A355841 616,   512,   84,    28;
%e A355841 1240,  744,   120,   40;
%e A355841 1936,  1928,  372,   136,  8;
%e A355841 3288,  2656,  616,   160;
%e A355841 4960,  4500,  1020,  332,  48;
%e A355841 7224,  6472,  1424,  392,  16;
%e A355841 9760,  11064, 2564,  824,  72,  16;
%e A355841 14144, 12424, 2696,  856,  32;
%e A355841 18312, 20604, 5308,  1468, 328, 16;
%e A355841 24384, 25392, 5968,  1584, 160, 8;
%e A355841 31816, 32768, 7564,  2652, 240, 16;
%e A355841 40456, 42240, 10384, 3064, 248, 24;
%e A355841 49384, 59152, 15068, 4680, 704, 64;
%e A355841 .
%e A355841 .
%Y A355841 Cf. A355838 (regions), A355839 (vertices), A355840 (edges), A355801 (without corner vertices), A290131, A331452, A335678.
%K A355841 nonn,tabf
%O A355841 1,1
%A A355841 _Scott R. Shannon_, Jul 18 2022