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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. 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 (list; graph; refs; listen; history; text; internal format)
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

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 (k-gons), 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

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Last modified January 28 22:08 EST 2023. Contains 359905 sequences. (Running on oeis4.)