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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
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.
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
KEYWORD
nonn,tabf
AUTHOR
Scott R. Shannon, Jul 22 2022
STATUS
approved