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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.
5
4, 40, 128, 44, 12, 320, 152, 24, 616, 512, 84, 28, 1240, 744, 120, 40, 1936, 1928, 372, 136, 8, 3288, 2656, 616, 160, 4960, 4500, 1020, 332, 48, 7224, 6472, 1424, 392, 16, 9760, 11064, 2564, 824, 72, 16, 14144, 12424, 2696, 856, 32, 18312, 20604, 5308, 1468, 328, 16, 24384, 25392, 5968, 1584, 160, 8
OFFSET
1,1
COMMENTS
This sequence is similar to A355801 but here the corner vertices of the square are also connected to points on the opposite edge.
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 A355838 for more images of the square.
EXAMPLE
The table begins:
4;
40;
128, 44, 12;
320, 152, 24;
616, 512, 84, 28;
1240, 744, 120, 40;
1936, 1928, 372, 136, 8;
3288, 2656, 616, 160;
4960, 4500, 1020, 332, 48;
7224, 6472, 1424, 392, 16;
9760, 11064, 2564, 824, 72, 16;
14144, 12424, 2696, 856, 32;
18312, 20604, 5308, 1468, 328, 16;
24384, 25392, 5968, 1584, 160, 8;
31816, 32768, 7564, 2652, 240, 16;
40456, 42240, 10384, 3064, 248, 24;
49384, 59152, 15068, 4680, 704, 64;
.
.
CROSSREFS
Cf. A355838 (regions), A355839 (vertices), A355840 (edges), A355801 (without corner vertices), A290131, A331452, A335678.
Sequence in context: A091104 A069539 A063997 * A187378 A199833 A248964
KEYWORD
nonn,tabf
AUTHOR
Scott R. Shannon, Jul 18 2022
STATUS
approved