A355992 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.

4, 24, 8, 56, 28, 12, 96, 80, 8, 4, 144, 140, 36, 12, 216, 216, 24, 4, 272, 332, 76, 24, 8, 360, 448, 80, 28, 456, 572, 132, 36, 8, 568, 728, 128, 64, 656, 916, 260, 28, 40, 4, 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

Offset

1,1

Comments

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.

See A108914 for more images of the square.

Links

Table of n, a(n) for n=1..68.

Scott R. Shannon, Image for n = 13.

Example

The table begins:
4;
24,   8;
56,   28,   12;
96,   80,   8,   4;
144,  140,  36,  12;
216,  216,  24,  4;
272,  332,  76,  24,  8;
360,  448,  80,  28;
456,  572,  132, 36,  8;
568,  728,  128, 64;
656,  916,  260, 28,  40, 4;
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;
.
.

Crossrefs

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

Sequence in context: A010294 A350887 A216923 * A233149 A169688 A222595

Adjacent sequences: A355989 A355990 A355991 * A355993 A355994 A355995

Keyword

nonn,tabf

Author

Scott R. Shannon, Jul 22 2022

Status

approved