A355992 - OEIS

%I #13 Jan 04 2024 14:10:23

%S 4,24,8,56,28,12,96,80,8,4,144,140,36,12,216,216,24,4,272,332,76,24,8,

%T 360,448,80,28,456,572,132,36,8,568,728,128,64,656,916,260,28,40,4,

%U 792,1104,176,36,928,1308,316,128,32,4,1064,1568,304,128,16,1240,1772,396,88,32,4,1416,2032,432,156,32

%N 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 four corner vertices to the points dividing the sides into n equal parts.

%C Up to n = 100 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 See A108914 for more images of the square.

%H Scott R. Shannon, <a href="/A355992/a355992.jpg">Image for n = 13</a>.

%e The table begins:

%e 4;

%e 24,   8;

%e 56,   28,   12;

%e 96,   80,   8,   4;

%e 144,  140,  36,  12;

%e 216,  216,  24,  4;

%e 272,  332,  76,  24,  8;

%e 360,  448,  80,  28;

%e 456,  572,  132, 36,  8;

%e 568,  728,  128, 64;

%e 656,  916,  260, 28,  40, 4;

%e 792,  1104, 176, 36;

%e 928,  1308, 316, 128, 32, 4;

%e 1064, 1568, 304, 128, 16;

%e 1240, 1772, 396, 88,  32, 4;

%e 1416, 2032, 432, 156, 32;

%e .

%e .

%Y Cf. A108914 (regions), A355948 (edges), A355949 (vertices), A355841, A331452, A335678.

%K nonn,tabf

%O 1,1

%A _Scott R. Shannon_, Jul 22 2022