A335614 Irregular table read by rows: row n gives the number of 4-gon to k-gon contacts, with k>=4, for a regular n-gon with all diagonals drawn.

0, 0, 0, 6, 0, 5, 24, 18, 36, 18, 90, 20, 110, 110, 44, 168, 208, 208, 52, 378, 140, 570, 330, 330, 640, 320, 32, 918, 646, 238, 34, 34, 990, 1254, 1330, 304, 38, 76, 1540, 1040, 80, 2478, 1722, 1008, 42, 2948, 1408, 44, 132, 132, 2852, 2254, 1012, 92, 46, 3624, 1536, 144

Offset: 3

Author

Scott R. Shannon, Aug 23 2020

Keywords

• nonn
• tabf

Comments

See A333654 for the number of 3-gon to k-gon contacts, with k>=3.

See A335646 for the number of 5-gon to k-gon contacts, with k>=5.

See A337330 for the number of 6-gon to k-gon contacts, with k>=6.

See A007678 for the number of regions and images of other n-gons.

Examples

			The table begins:
.
0;
0;
0;
6;
0,5;
24;
18,36,18;
90,20;
110,110,44;
168;
208,208,52;
378,140;
570,330,330;
640,320,32;
918,646,238,34,34;
990;
1254,1330,304,38,76;
1540,1040,80;
2478,1722,1008,42;
2948,1408,44,132,132;
2852,2254,1012,92,46;
3624,1536,144;
4650,3600,1450,150,150;
4784,3380,572,52;
6696,4968,2160,54,54;
7280,3752,2072,168;
8990,7308,3016,0,232,0,0,58;
7770,1200,300;
13020,9920,3472,186,434,0,124;
12160,8576,2048,256;
14784,11418,5742,792,330;
		

Links

• Scott R. Shannon, Image for n=6 with edge-number coloring. This is the first n-gon with 4-gon to 4-gon contacts.
• Scott R. Shannon, Image for n=7 with edge-number coloring. This is the first n-gon with 4-gon to 5-gon contacts.
• Scott R. Shannon, Image for n=9 with edge-number coloring. This is the first n-gon with 4-gon to 6-gon contacts.
• Scott R. Shannon, Image for n=17 with edge-number coloring. This is the first n-gon with 4-gon to 7-gon and 4-gon to 8-gon contacts.
• Scott R. Shannon, Image for n=31 with edge-number coloring. This is the first n-gon with 4-gon to 10-gon contacts.
• Scott R. Shannon, Image for n=31 with random distance-based coloring.
• Scott R. Shannon, Image for n=29 with edge-number coloring. This is the first n-gon with 4-gon to 11-gon contacts.
• Scott R. Shannon, Image for n=18 with edge-number coloring. This is the only n-gon from n=13 to n=33 that has only 4-gon to 3-gon and 4-gon to 4-gon contacts. It is likely the last n-gon with this property.
• Scott R. Shannon, Image for n=18 with random distance-based coloring.

Crossrefs

Cf. A333654 (3-gon contacts), A335646 (5-gon contacts), , A337330 (6-gon contacts), A007678, A135565, A007569, A062361, A331450, A331451.