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

3,4

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.

Links

Table of n, a(n) for n=3..60.

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.

Example

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;

Crossrefs

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

Sequence in context: A343948 A195368 A198426 * A019110 A280508 A217221

Adjacent sequences: A335611 A335612 A335613 * A335615 A335616 A335617

Keyword

nonn,tabf

Author

Scott R. Shannon, Aug 23 2020

Status

approved