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A333654 Irregular table read by rows: row n gives the number of 3-gon to k-gon contacts, with k>=3, for a regular n-gon with all diagonals drawn.

%I A333654 #37 Aug 29 2020 02:51:50
%S A333654 0,4,10,0,5,18,12,28,14,21,0,7,56,48,54,54,54,36,0,0,9,180,160,30,88,
%T A333654 154,88,88,0,0,0,0,11,240,336,130,260,299,182,0,104,0,0,0,0,13,266,
%U A333654 616,266,180,600,375,300,90,0,0,0,0,0,0,0,15,448,1056,320,256
%N A333654 Irregular table read by rows: row n gives the number of 3-gon to k-gon contacts, with k>=3, for a regular n-gon with all diagonals drawn.
%C A333654 See A335614 for the number of 4-gon to k-gon contacts, with k>=4.
%C A333654 See A335646 for the number of 5-gon to k-gon contacts, with k>=5.
%C A333654 See A337330 for the number of 6-gon to k-gon contacts, with k>=6.
%C A333654 See A007678 for the number of regions and images of other n-gons.
%H A333654 Scott R. Shannon, <a href="/A333654/a333654.png">Image for n=4 with edge-count coloring</a>. This is the first n-gon with 3-gon to 3-gon contacts.
%H A333654 Scott R. Shannon, <a href="/A333654/a333654_1.png">Image for n=6 with edge-count coloring</a>. This is the first n-gon with 3-gon to 4-gon contacts.
%H A333654 Scott R. Shannon, <a href="/A333654/a333654_2.png">Image for n=7 with edge-count coloring</a>. This is the first n-gon with 3-gon to 5-gon contacts, other than n=5 which has an internal 5-gon surrounded by 3-gons by its construction.
%H A333654 Scott R. Shannon, <a href="/A333654/a333654_3.png">Image for n=9 with edge-count coloring</a>. This is the first n-gon with 3-gon to 6-gon contacts.
%H A333654 Scott R. Shannon, <a href="/A333654/a333654_4.png">Image for n=15 with edge-count coloring</a>. This is the first n-gon with 3-gon to 7-gon contacts, other than n=7 which has an internal 7-gon surrounded by 3-gons by its construction.
%H A333654 Scott R. Shannon, <a href="/A333654/a333654_8.png">Image for n=15 with random distance-based coloring</a>.
%H A333654 Scott R. Shannon, <a href="/A333654/a333654_6.png">Image for n=13 with edge-count coloring</a>. This is the first n-gon with 3-gon to 8-gon contacts.
%H A333654 Scott R. Shannon, <a href="/A333654/a333654_7.png">Image for n=29 with edge-count coloring</a>. This is the first n-gon with 3-gon to 10-gon and 3-gon to 11-gon contacts.
%F A333654 For odd n, with n > 3, row(n,n) = n as the n-gon contains a smaller n-gon at its center surrounded by 3-gons.
%e A333654 The table begins:
%e A333654 .
%e A333654 0;
%e A333654 4;
%e A333654 10,0,5;
%e A333654 18,12;
%e A333654 28,14,21,0,7;
%e A333654 56,48;
%e A333654 54,54,54,36,0,0,9;
%e A333654 180,160,30;
%e A333654 88,154,88,88,0,0,0,0,11;
%e A333654 240,336;
%e A333654 130,260,299,182,0,104,0,0,0,0,13;
%e A333654 266,616,266;
%e A333654 180,600,375,300,90,0,0,0,0,0,0,0,15;
%e A333654 448,1056,320,256;
%e A333654 238,816,935,578,85,238,0,0,0,0,0,0,0,0,17;
%e A333654 900,1836,324,108,126;
%e A333654 304,1520,1463,798,304,228,0,0,0,0,0,0,0,0,0,0,19;
%e A333654 1000,2120,1740,560,0,160;
%e A333654 378,2352,2016,1554,84,0,0,0,0,0,0,0,0,0,0,0,0,0,21;
%e A333654 1056,3828,2310,308,176,220;
%e A333654 460,2852,4117,2530,644,138,0,0,0,0,0,0,0,0,0,0,0,0,0,0,23;
%e A333654 2352,5856,2376,288;
%e A333654 550,4550,4800,3350,900,250,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,25;
%e A333654 1950,6708,5772,1612,650,208;
%e A333654 648,6372,6399,4968,432,810,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,27;
%e A333654 2380,10024,5712,3584,616,224;
%e A333654 754,8642,8497,6148,783,928,0,870,232,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,29;
%e A333654 6330,14640,5340,2340;
%e A333654 868,11532,11191,7378,806,1302,0,496,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,31;
%e A333654 3712,16384,12000,6016,1248;
%e A333654 990,14454,14619,12540,2079,1782,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,33;
%Y A333654 Cf. A335614 (4-gon contacts), A335646 (5-gon contacts), A337330 (6-gon contacts), A007678, A135565, A007569, A062361, A331450, A331451.
%K A333654 nonn,tabf
%O A333654 3,2
%A A333654 _Scott R. Shannon_, Aug 23 2020