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Irregular table read by rows: row n gives the number of 6-gon to k-gon contacts, with k>=6, for a regular n-gon with all diagonals drawn, with n>=25.
6

%I #15 Jan 11 2021 23:13:32

%S 50,0,108,0,0,0,124,32,66,136,70,144,148,76,390,120,328,82,42,86,86,0,

%T 540,92,92,188,94,94,0,196,98,750,100,816,416,104,1272,432,220,110,

%U 728,570,570,406,348,116,1062,354,300,854,366,122,1488,124,1512,252,126,576,2080,130,260,2112

%N Irregular table read by rows: row n gives the number of 6-gon to k-gon contacts, with k>=6, for a regular n-gon with all diagonals drawn, with n>=25.

%C For n=3 to n=24 there are no n-gons that have 6-gon to k-gon contacts, where k>=6, so the table starts at n=25.

%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 A335646 for the number of 5-gon to k-gon contacts, with k>=5.

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

%H Scott R. Shannon, <a href="/A337330/a337330.png">Image for n=25 with edge-number coloring</a>. This is the first n-gon with 6-gon to 6-gon contacts.

%H Scott R. Shannon, <a href="/A337330/a337330_1.png">Image for n=25 with random distance-based coloring</a>.

%e The table begins:

%e .

%e 50;

%e 0;

%e 108;

%e 0;

%e 0;

%e 0;

%e 124;

%e 32;

%e 66;

%e 136;

%e 70;

%e 144;

%e 148;

%e 76;

%e 390;

%e 120;

%e 328, 82;

%e 42;

%Y Cf. A333654 (3-gon contacts), A335614 (4-gon contacts), A335646 (5-gon contacts), A007678, A135565, A007569, A062361, A331450, A331451.

%K nonn,tabf

%O 25,1

%A _Scott R. Shannon_, Aug 23 2020

%E a(34) and beyond from _Scott R. Shannon_, Jan 11 2021