A374828 Irregular table read by rows: Place n equally spaced points on the circumference of a circle of radius r and then connect each pair of points with straight lines whose intersections create A007569(n) - n additional points. Draw a circle of radius r around each of the A007569(n) points. T(n,k) is the number of k-sided regions, k>=2, formed from all circle intersections.

3, 3, 0, 12, 4, 5, 45, 10, 10, 10, 0, 156, 84, 48, 30, 6, 0, 742, 476, 294, 119, 21, 14, 0, 1104, 1296, 512, 152, 40, 16, 0, 6669, 6768, 2790, 1179, 207, 81, 9, 0, 10280, 11130, 5490, 1440, 260, 150, 20, 10, 0, 40777, 45342, 20669, 6963, 1177, 374, 77, 11, 11

Offset: 3

Author

Scott R. Shannon, Jul 21 2024

Keywords

• nonn
• tabf

Comments

It is likely that n = 5 is the last graph that produces 2-sided regions, although this is unknown.

Examples

			The table begins:
3, 3;
0, 12, 4;
5, 45, 10, 10, 10;
0, 156, 84, 48, 30, 6;
0, 742, 476, 294, 119, 21, 14;
0, 1104, 1296, 512, 152, 40, 16;
0, 6669, 6768, 2790, 1179, 207, 81, 9;
0, 10280, 11130, 5490, 1440, 260, 150, 20, 10;
0, 40777, 45342, 20669, 6963, 1177, 374, 77, 11, 11;
0, 33672, 39552, 16236, 5772, 1080, 288, 0, 12, 0, 12;
0, 181467, 212186, 97461, 30082, 5252, 1430, 78, 104, 0, 0, 13;
0, 198772, 246134, 104356, 33348, 5614, 1190, 252, 28, 0, 0, 0, 14;
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Links

• Scott R. Shannon, Image for n = 5. The starting circles' centers are shown as white dots.
• Scott R. Shannon, Image for n = 7.

Crossrefs

Cf. A374825 (vertices), A374826 (regions), A374827 (edges), A007569 (total circles).

Formula

Sum of row n = A374826(n).