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

3,1

Comments

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

Links

Table of n, a(n) for n=3..59.

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

Scott R. Shannon, Image for n = 7.

Formula

Sum of row n = A374826(n).

Example

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;
.
.

Crossrefs

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

Sequence in context: A262292 A100543 A039928 * A247889 A309012 A137259

Adjacent sequences: A374825 A374826 A374827 * A374829 A374830 A374831

Keyword

nonn,tabf

Author

Scott R. Shannon, Jul 21 2024

Status

approved