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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. 6
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 23 12:51 EST 2022. Contains 350511 sequences. (Running on oeis4.)