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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.
7
0, 1, 0, 4, 12, 12, 56, 32, 16, 156, 124, 24, 8, 0, 4, 384, 228, 72, 28, 716, 648, 144, 68, 8, 4, 1312, 1144, 240, 112, 8, 2244, 1912, 528, 256, 3528, 3072, 696, 360, 16, 5012, 5536, 1296, 524, 48, 28, 7696, 6596, 1960, 572, 16, 10340, 11448, 2968, 1028, 160, 24, 14520, 14428, 3872, 1156, 104, 8
OFFSET
1,4
COMMENTS
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.
See A355798 for more images of the square.
The keyword "look" is for the n = 10 image. - N. J. A. Sloane, Jul 21 2022
EXAMPLE
The table begins:
0, 1;
0, 4;
12, 12;
56, 32, 16;
156, 124, 24, 8, 0, 4;
384, 228, 72, 28;
716, 648, 144, 68, 8, 4;
1312, 1144, 240, 112, 8;
2244, 1912, 528, 256;
3528, 3072, 696, 360, 16;
5012, 5536, 1296, 524, 48, 28;
7696, 6596, 1960, 572, 16;
10340, 11448, 2968, 1028, 160, 24;
14520, 14428, 3872, 1156, 104, 8;
19588, 19156, 5296, 2052, 160, 8;
25392, 26112, 7160, 2152, 208, 24;
31820, 37244, 9936, 3240, 488, 64;
.
.
CROSSREFS
Cf. A355798 (regions), A355799 (vertices), A355800 (edges), A355801 (k-gons), A255011 (all vertices), A290131, A331452, A335678.
Sequence in context: A209019 A202636 A239194 * A357727 A009115 A051434
KEYWORD
nonn,tabf,look
AUTHOR
Scott R. Shannon, Jul 17 2022
STATUS
approved