A371274 Irregular table read by rows: T(n,k) is the number of k-sided regions, k>=2, formed when n equally spaced points are placed around a circle and all pairs of points are joined by an interior arc whose radius equals the circle's radius.

1, 3, 3, 4, 0, 1, 10, 10, 5, 1, 12, 6, 14, 56, 21, 0, 7, 1, 8, 48, 32, 0, 0, 0, 1, 27, 144, 54, 27, 18, 10, 160, 70, 0, 30, 0, 0, 0, 1, 22, 253, 330, 11, 33, 0, 0, 0, 0, 1, 12, 276, 204, 0, 24, 26, 624, 403, 130, 104, 0, 0, 0, 0, 0, 0, 1, 14, 630, 448, 112, 70, 14, 14, 0, 0, 0, 0, 0, 1, 45, 960, 915, 165, 165

Offset

2,2

Comments

See A371253 and A371254 for images.

Links

Table of n, a(n) for n=2..85.

Formula

Sum of row n = A371253(n).

Example

The table begins:
1;
3, 3;
4, 0, 1;
10, 10, 5, 1;
12, 6;
14, 56, 21, 0, 7, 1;
8, 48, 32, 0, 0, 0, 1;
27, 144, 54, 27, 18;
10, 160, 70, 0, 30, 0, 0, 0, 1;
22, 253, 330, 11, 33, 0, 0, 0, 0, 1;
12, 276, 204, 0, 24;
26, 624, 403, 130, 104, 0, 0, 0, 0, 0, 0, 1;
14, 630, 448, 112, 70, 14, 14, 0, 0, 0, 0, 0, 1;
45, 960, 915, 165, 165;
16, 1136, 704, 272, 192, 0, 16, 0, 0, 0, 0, 0, 0, 0, 1;
34, 1581, 1870, 238, 272, 17, 34, 0, 0, 0, 0, 0, 0, 0, 0, 1;
18, 1656, 1386, 270, 288, 0, 18;
38, 2622, 2546, 646, 513, 38, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
20, 2680, 2420, 820, 380, 20, 60, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
63, 3297, 4725, 1050, 315, 42, 105;
22, 3696, 4136, 1342, 484, 22, 66, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;

Crossrefs

Cf. A371253 (regions), A371254 (vertices), A371255 (edges), A331450, A359009, A359061, A359258.

Sequence in context: A230667 A131462 A230811 * A117032 A243823 A281141

Adjacent sequences: A371271 A371272 A371273 * A371275 A371276 A371277

Keyword

nonn,tabf

Author

Scott R. Shannon, Mar 17 2024

Status

approved