A372734 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 when every pair of the 3 + 3*n points are connected by a circle and where the points lie at the ends of the circle's diameter.

0, 7, 12, 61, 9, 6, 6, 303, 108, 9, 9, 3, 18, 771, 603, 150, 15, 9, 0, 1, 24, 1722, 1740, 339, 81, 3, 0, 1, 30, 3789, 4326, 1104, 234, 18, 3, 36, 6907, 8274, 2193, 432, 45, 18, 66, 12012, 15504, 4173, 922, 105, 45, 3, 3, 90, 19860, 24774, 7389, 1773, 150, 30, 48, 30594, 39852, 12438, 2998, 387, 48

Offset: 0

Author

Scott R. Shannon, May 12 2024

Keywords

• nonn
• tabf

Comments

A circle is constructed for every pair of the 3 + 3*n points, the two points lying at the ends of a diameter of the circle.

See A372731 and A372732 for images of the circles.

Examples

			The table begins:
0, 7;
12, 61, 9, 6;
6, 303, 108, 9, 9, 3;
18, 771, 603, 150, 15, 9, 0, 1;
24, 1722, 1740, 339, 81, 3, 0, 1;
30, 3789, 4326, 1104, 234, 18, 3;
36, 6907, 8274, 2193, 432, 45, 18;
66, 12012, 15504, 4173, 922, 105, 45, 3, 3;
90, 19860, 24774, 7389, 1773, 150, 30;
48, 30594, 39852, 12438, 2998, 387, 48;
96, 45456, 59019, 18669, 4429, 609, 93, 3, 6;
90, 66633, 86088, 29136, 6840, 1164, 195, 6;
120, 90210, 121614, 40035, 9160, 1362, 177, 12, 9;
108, 124245, 167646, 57048, 14377, 1989, 300, 33, 15;
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Crossrefs

Cf. A372731 (vertices), A372732 (regions), A372733 (edges), A372735 (number of circles), A372617, A371376, A361623, A360354.

Formula

Sum of row(n) = A372732(n).