A368816 Irregular table read by rows: T(n,k) is the number of k-gons, k>=3, in a regular 2n-gon when all vertices are connect by straight lines except for the n lines joining diametrically opposite vertices.

0, 0, 1, 12, 0, 0, 1, 40, 8, 8, 0, 0, 1, 100, 40, 20, 10, 0, 0, 0, 1, 204, 132, 12, 12, 0, 0, 0, 0, 0, 1, 378, 280, 126, 28, 0, 0, 0, 0, 0, 0, 0, 1, 688, 528, 176, 96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1188, 864, 72, 54, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

Offset

1,4

Comments

See A368813 and A368814 for other images of the 2n-gons.

Links

Table of n, a(n) for n=1..73.

Scott R. Shannon, Image for T(7,k).

Scott R. Shannon, Table for n = 1..100.

Formula

Sum of row n = A368813(n).

Example

The table begins:
0;
0, 1;
12, 0, 0, 1;
40, 8, 8, 0, 0, 1;
100, 40, 20, 10, 0, 0, 0, 1;
204, 132, 12, 12, 0, 0, 0, 0, 0, 1;
378, 280, 126, 28, 0, 0, 0, 0, 0, 0, 0, 1;
688, 528, 176, 96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
1188, 864, 72, 54, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
1840, 1360, 620, 220, 20, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
2508, 2552, 880, 198, 44, 66, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
3648, 3576, 864, 216, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
.
.

Crossrefs

Cf. A368813 (regions), A368814 (vertices), A368815 (edges), A368755, A368758.

Sequence in context: A242240 A225341 A369349 * A004012 A360223 A270256

Adjacent sequences: A368813 A368814 A368815 * A368817 A368818 A368819

Keyword

nonn,tabf

Author

Scott R. Shannon, Jan 06 2024

Status

approved