A367665 Irregular table read by rows: T(n,k) is the number of k-sided polygons, for n>=1 and k>=3, in a hexagon when straight line segments connect the n-1 points between each corner that divide each edge into n equal parts to the n-1 points on the edge on the opposite side of the hexagon.

0, 0, 0, 1, 0, 6, 30, 12, 12, 126, 102, 6, 18, 384, 294, 78, 18, 0, 6, 888, 726, 300, 42, 12, 1824, 1500, 594, 216, 12, 3186, 3048, 1206, 186, 36, 5592, 4914, 1866, 588, 48, 6, 8736, 8298, 3108, 816, 108, 12, 13164, 12786, 5046, 1368, 180, 18, 19578, 17940, 7242, 1854, 144, 60, 26700, 27426, 10842, 2652, 324, 18

Offset: 1

Author

Scott R. Shannon, Nov 26 2023

Keywords

• nonn
• tabf

Examples

			The table begins:
0, 0, 0, 1;
0, 6;
30, 12, 12;
126, 102, 6, 18;
384, 294, 78, 18, 0, 6;
888, 726, 300, 42, 12;
1824, 1500, 594, 216, 12;
3186, 3048, 1206, 186, 36;
5592, 4914, 1866, 588, 48, 6;
8736, 8298, 3108, 816, 108, 12;
13164, 12786, 5046, 1368, 180, 18;
19578, 17940, 7242, 1854, 144, 60;
26700, 27426, 10842, 2652, 324, 18;
36972, 37134, 15000, 3462, 408, 72;
50316, 48552, 19398, 4830, 480, 96, 0, 12;
64398, 68388, 27018, 6006, 852, 132;
83052, 89268, 35178, 8526, 1140, 204, 12;
106956, 109938, 42600, 10218, 1116, 204, 24;
131664, 145332, 56622, 14160, 1908, 234, 12;
166338, 173514, 69426, 16716, 2004, 252;
202932, 215028, 82374, 20202, 2400, 324, 12;
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Links

• Scott R. Shannon, Image for T(9,k).

Crossrefs

Cf. A367662 (regions), A367663 (vertices), A367664 (edges), A355801.

Formula

Sum of row(n) = A367662(n).