A335646 Irregular table read by rows: row n gives the number of 5-gon to k-gon contacts, with k>=5, for a regular n-gon with all diagonals drawn.

0, 0, 0, 0, 0, 0, 0, 0, 11, 0, 39, 42, 15, 0, 15, 0, 102, 18, 190, 38, 19, 20, 80, 273, 210, 21, 154, 44, 529, 322, 69, 144, 750, 350, 598, 156, 26, 1215, 432, 81, 560, 56, 928, 406, 29, 0, 0, 0, 29, 300, 60, 2139, 248, 93, 1568, 704, 64, 1782, 792, 132

Offset

3,9

Comments

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

See A335614 for the number of 4-gon to k-gon contacts, with k>=4.

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..62.

Scott R. Shannon, Image for n=11 with edge-number coloring. This is the first n-gon with 5-gon to 5-gon contacts.

Scott R. Shannon, Image for n=19 with edge-number coloring. This is the first n-gon with 5-gon to 6-gon contacts. It is also the first n-gon with 7-gon to 7-gon contacts.

Scott R. Shannon, Image for n=15 with edge-number coloring. This is the first n-gon with 5-gon to 7-gon contacts.

Scott R. Shannon, Image for n=29 with edge-number coloring. This is the first n-gon with 5-gon to 11-gon contacts.

Scott R. Shannon, Image for n=29 with random distance-based coloring.

Example

The table begins:
.
0;
0;
0;
0;
0;
0;
0;
0;
11;
0;
39;
42;
15,0,15;
0;
102;
18;
190,38,19;
20,80;
273,210,21;
154,44;
529,322,69;
144;
750,350;
598,156,26;
1215,432,81;
560,56;
928,406,29,0,0,0,29;
300,60;
2139,248,93;
1568,704,64;
1782,792,132;

Crossrefs

Cf. A333654 (3-gon contacts), A335614 (4-gon contacts), A337330 (6-gon contacts), A007678, A135565, A007569, A062361, A331450, A331451.

Sequence in context: A087555 A185682 A217752 * A261173 A287468 A110417

Adjacent sequences: A335643 A335644 A335645 * A335647 A335648 A335649

Keyword

nonn,tabf

Author

Scott R. Shannon, Aug 23 2020

Status

approved