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Irregular table read by rows: row n gives the number of 7-gon to k-gon contacts, with k>=7, for a regular n-gon with all diagonals drawn, with n>=19.
1

%I #17 Jan 15 2021 21:12:43

%S 19,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,

%T 52,0,0,0,0,0,0,0,118,0,61,0,63,0,0,0,0,0,138,70,0,72,73,148,0,0,0,0,

%U 158,80,0,82,83,0,0,172,0,0,178,540,0,0,93,0,93,282,95,96,194,294,0,198,99

%N Irregular table read by rows: row n gives the number of 7-gon to k-gon contacts, with k>=7, for a regular n-gon with all diagonals drawn, with n>=19.

%C For n=3 to n=18 there are no n-gons that have 7-gon to k-gon contacts, where k>=7, so the table starts at n=19.

%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 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="/A340650/a340650.png">Image for n = 19</a>. This is the first n-gon with 7-gon to 7-gon contacts.

%H Scott R. Shannon, <a href="/A340650/a340650_1.png">Image for n = 59</a>. This is the first n-gon with 7-gon to 8-gon contacts.

%e a(19) = 19, a(20-51) = 0, a(52) = 52, a(53-58) = 0.

%e The table from a(59) begins:

%e 0, 118,

%e 9;

%e 61;

%e 0;

%e 63;

%e 0;

%e 0;

%e 0;

%e 0;

%e 0;

%e 138;

%e 70;

%e 0;

%e 72;

%e 73;

%e 148;

%e 0;

%e 0;

%e 0;

%e 0;

%e 158;

%e 80;

%e 0;

%e 82;

%e 83;

%e 0;

%e 0;

%e 172;

%e 0;

%e 0;

%e 178;

%e 540;

%e 0;

%e 0;

%e 93, 0, 93;

%e 282;

%e 95;

%e 96;

%e 194;

%e 294;

%e 0, 198, 99;

%e 0;

%Y Cf. A333654 (3-gon contacts), A335614 (4-gon contacts), A335646 (5-gon contacts), A337330 (6-gon contacts), A007678, A135565, A007569, A062361, A331450, A331451.

%K nonn,tabf

%O 19,1

%A _Scott R. Shannon_, Jan 14 2021