

A355801


Irregular table read by rows: T(n,k) is the number of ksided polygons, for k>=3, in a square when straight line segments connect the n1 points between each corner that divide each edge into n equal parts to the n1 points on the edge on the opposite side of the square.


6



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
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OFFSET

1,4


COMMENTS

Up to n = 50 the maximum sided kgon created is the 8gon. It is plausible this is the maximum sided kgon 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


LINKS

Table of n, a(n) for n=1..62.
Scott R. Shannon, Image for n = 10.


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 (kgons), A255011 (all vertices), A290131, A331452, A335678.
Sequence in context: A209019 A202636 A239194 * A357727 A009115 A051434
Adjacent sequences: A355798 A355799 A355800 * A355802 A355803 A355804


KEYWORD

nonn,look


AUTHOR

Scott R. Shannon, Jul 17 2022


STATUS

approved



