A372617 Irregular table read by rows: T(n,k) is the number of k-gons, k>=2, among all distinct circles that can be constructed from the 3 vertices and the equally spaced 3*n points placed on the sides of an equilateral triangle, using only a compass.

0, 7, 3, 70, 45, 3, 6, 312, 273, 33, 6, 1017, 1119, 186, 36, 3, 0, 1, 6, 2943, 4092, 702, 150, 15, 3, 1, 6, 6210, 8556, 1941, 351, 45, 3, 3, 6, 12946, 20034, 4632, 735, 99, 9, 6, 20925, 32685, 7944, 1435, 162, 27, 18, 37704, 59520, 15375, 2589, 324, 84, 30, 55326, 87138, 22626, 4456, 474, 96, 3

Offset: 0

Author

Scott R. Shannon, May 07 2024

Keywords

• nonn
• tabf

Comments

A circle is constructed for every pair of the 3 + 3*n points, the first point defines the circle's center while the second the radius distance.

See A372614 and A372615 for images of the circles.

Examples

			The table begins:
0, 7;
3, 70, 45, 3;
6, 312, 273, 33;
6, 1017, 1119, 186, 36, 3, 0, 1;
6, 2943, 4092, 702, 150, 15, 3, 1;
6, 6210, 8556, 1941, 351, 45, 3, 3;
6, 12946, 20034, 4632, 735, 99, 9;
6, 20925, 32685, 7944, 1435, 162, 27;
18, 37704, 59520, 15375, 2589, 324, 84;
30, 55326, 87138, 22626, 4456, 474, 96, 3;
30, 91923, 146121, 38817, 7777, 894, 135, 9, 9;
36, 118734, 189804, 51747, 10356, 1122, 183;
36, 185730, 299571, 84285, 16015, 2139, 261, 3, 3;
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Crossrefs

Cf. A372614 (vertices), A372615 (regions), A372616 (edges), A372682 (number of circles), A371376, A361623, A360354.

Formula

Sum of row n = A372615(n).