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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.
6

%I #27 Aug 29 2020 02:52:36

%S 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,

%T 21,154,44,529,322,69,144,750,350,598,156,26,1215,432,81,560,56,928,

%U 406,29,0,0,0,29,300,60,2139,248,93,1568,704,64,1782,792,132

%N 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.

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

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

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

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

%H Scott R. Shannon, <a href="/A335646/a335646.png">Image for n=11 with edge-number coloring</a>. This is the first n-gon with 5-gon to 5-gon contacts.

%H Scott R. Shannon, <a href="/A335646/a335646_2.png">Image for n=19 with edge-number coloring</a>. 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.

%H Scott R. Shannon, <a href="/A335646/a335646_1.png">Image for n=15 with edge-number coloring</a>. This is the first n-gon with 5-gon to 7-gon contacts.

%H Scott R. Shannon, <a href="/A335646/a335646_3.png">Image for n=29 with edge-number coloring</a>. This is the first n-gon with 5-gon to 11-gon contacts.

%H Scott R. Shannon, <a href="/A335646/a335646_4.png">Image for n=29 with random distance-based coloring</a>.

%e The table begins:

%e .

%e 0;

%e 0;

%e 0;

%e 0;

%e 0;

%e 0;

%e 0;

%e 0;

%e 11;

%e 0;

%e 39;

%e 42;

%e 15,0,15;

%e 0;

%e 102;

%e 18;

%e 190,38,19;

%e 20,80;

%e 273,210,21;

%e 154,44;

%e 529,322,69;

%e 144;

%e 750,350;

%e 598,156,26;

%e 1215,432,81;

%e 560,56;

%e 928,406,29,0,0,0,29;

%e 300,60;

%e 2139,248,93;

%e 1568,704,64;

%e 1782,792,132;

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

%K nonn,tabf

%O 3,9

%A _Scott R. Shannon_, Aug 23 2020