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

Author

Scott R. Shannon, Jan 06 2024

Keywords

• nonn
• tabf

Comments

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

Examples

			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;
.
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Links

• Scott R. Shannon, Image for T(7,k).
• Scott R. Shannon, Table for n = 1..100.

Crossrefs

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

Formula

Sum of row n = A368813(n).