A062361 -id:A062361 - cp's OEIS frontend

A291949 Number of maximal cliques in the n-polygon diagonal intersection graph.

1, 4, 10, 24, 49, 80, 162, 230, 451, 444, 884, 1036, 1845, 1840, 3026, 2412, 4921, 4960, 8022, 7854, 10925, 9864, 16150, 15860, 22545, 22204, 30218, 21300, 41261, 39776, 51678, 51102, 67025, 58680, 83990, 82802, 104715, 102480, 126362, 107184, 155445, 152020

Offset: 3

Eric W. Weisstein, Mar 09 2018

nonn

Maximal cliques in the n-polygon diagonal intersection graph are either triangles or edges that are not contained in a triangle. - Andrew Howroyd, Mar 11 2018

Andrew Howroyd, Table of n, a(n) for n = 3..100
Eric Weisstein's World of Mathematics, Maximal Clique
Eric Weisstein's World of Mathematics, Polygon Diagonal Intersection Graph

Cf. A062361, A135565, A300524.

Terms a(15) and beyond from Andrew Howroyd, Mar 11 2018

A300524 Number of (not necessarily maximal) cliques in the n-polygon diagonal intersection graph.

Original entry on oeis.org

8, 18, 41, 80, 169, 250, 514, 682, 1233, 1346, 2614, 2970, 4801, 5330, 8348, 7580, 13472, 14422, 20455, 21738, 30591, 28082, 43276, 45294, 59806, 62050, 80911, 66812, 106393, 110114, 139162, 142972, 177416, 171434, 223851, 228876, 278500

Offset: 3

Eric W. Weisstein, Mar 08 2018

nonn

Equal to 1 + vertex count + edge count + triangle count.

Eric Weisstein's World of Mathematics, Clique
Eric Weisstein's World of Mathematics, Polygon Diagonal Intersection Graph

Cf. A007569 (vertex count).
Cf. A062361 (edge count).
Cf. A135565 (triangle count).

a(n) = 1 + A007569(n) + A062361(n) + A135565(n).

A340650 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.

Original entry on oeis.org

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, 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, 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

Offset: 19

Scott R. Shannon, Jan 14 2021

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

			a(19) = 19, a(20-51) = 0, a(52) = 52, a(53-58) = 0.
The table from a(59) begins:
0, 118,
9;
61;
0;
63;
0;
0;
0;
0;
0;
138;
70;
0;
72;
73;
148;
0;
0;
0;
0;
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;
0;

Scott R. Shannon, Image for n = 19. This is the first n-gon with 7-gon to 7-gon contacts.
Scott R. Shannon, Image for n = 59. This is the first n-gon with 7-gon to 8-gon contacts.

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

cp's OEIS Frontend

A291949 Number of maximal cliques in the n-polygon diagonal intersection graph.

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A300524 Number of (not necessarily maximal) cliques in the n-polygon diagonal intersection graph.

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A340650 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.

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