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

1,6

Links

Table of n, a(n) for n=1..64.

Scott R. Shannon, Image for T(9,k).

Formula

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

Example

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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Crossrefs

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

Sequence in context: A051685 A326858 A165734 * A309253 A260017 A351773

Adjacent sequences: A367662 A367663 A367664 * A367666 A367667 A367668

Keyword

nonn,tabf

Author

Scott R. Shannon, Nov 26 2023

Status

approved