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.

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

19,1

Comments

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.

Links

Table of n, a(n) for n=19..104.

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.

Example

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;

Crossrefs

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

Sequence in context: A259327 A271975 A186729 * A226373 A240952 A221749

Adjacent sequences: A340647 A340648 A340649 * A340651 A340652 A340653

Keyword

nonn,tabf

Author

Scott R. Shannon, Jan 14 2021

Status

approved