

A335614


Irregular table read by rows: row n gives the number of 4gon to kgon contacts, with k>=4, for a regular ngon 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
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OFFSET

3,4


COMMENTS

See A333654 for the number of 3gon to kgon contacts, with k>=3.
See A335646 for the number of 5gon to kgon contacts, with k>=5.
See A337330 for the number of 6gon to kgon contacts, with k>=6.
See A007678 for the number of regions and images of other ngons.


LINKS

Table of n, a(n) for n=3..60.
Scott R. Shannon, Image for n=6 with edgenumber coloring. This is the first ngon with 4gon to 4gon contacts.
Scott R. Shannon, Image for n=7 with edgenumber coloring. This is the first ngon with 4gon to 5gon contacts.
Scott R. Shannon, Image for n=9 with edgenumber coloring. This is the first ngon with 4gon to 6gon contacts.
Scott R. Shannon, Image for n=17 with edgenumber coloring. This is the first ngon with 4gon to 7gon and 4gon to 8gon contacts.
Scott R. Shannon, Image for n=31 with edgenumber coloring. This is the first ngon with 4gon to 10gon contacts.
Scott R. Shannon, Image for n=31 with random distancebased coloring.
Scott R. Shannon, Image for n=29 with edgenumber coloring. This is the first ngon with 4gon to 11gon contacts.
Scott R. Shannon, Image for n=18 with edgenumber coloring. This is the only ngon from n=13 to n=33 that has only 4gon to 3gon and 4gon to 4gon contacts. It is likely the last ngon with this property.
Scott R. Shannon, Image for n=18 with random distancebased 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 (3gon contacts), A335646 (5gon contacts), , A337330 (6gon 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



