A359258 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 n equally spaced points along a line using only a compass.

3, 0, 8, 4, 2, 0, 22, 23, 4, 2, 0, 50, 52, 12, 2, 0, 110, 103, 36, 6, 0, 190, 200, 64, 12, 0, 314, 387, 88, 28, 4, 0, 498, 606, 152, 32, 8, 0, 770, 941, 228, 58, 4, 2, 0, 1132, 1352, 338, 68, 12, 2, 0, 1602, 1935, 532, 98, 4, 0, 2122, 2798, 684, 106, 16, 0, 2850, 3843, 940, 132, 24, 6

Offset: 2

Author

Scott R. Shannon, Dec 23 2022

Keywords

• nonn
• tabf

Comments

A circle is constructed for every pair of the n points, the first point defines the circle's center while the second the radius distance. The number of distinct circles constructed for n points is A001859(n-1).

See A359252 and A359253 for other images of the circles.

Examples

			The table begins:
  3;
  0,     8,     4,    2;
  0,    22,    23,    4,   2;
  0,    50,    52,   12,   2;
  0,   110,   103,   36,   6;
  0,   190,   200,   64,  12;
  0,   314,   387,   88,  28,  4;
  0,   498,   606,  152,  32,  8;
  0,   770,   941,  228,  58,  4,  2;
  0,  1132,  1352,  338,  68, 12,  2;
  0,  1602,  1935,  532,  98,  4;
  0,  2122,  2798,  684, 106, 16;
  0,  2850,  3843,  940, 132, 24,  6;
  0,  3774,  4998, 1268, 192, 28,  6;
  0,  4950,  6475, 1644, 276, 44, 10;
  0,  6190,  8454, 1978, 326, 74,  4;
  0,  7778, 10737, 2520, 434, 52, 12, 4;
  0,  9674, 13224, 3202, 528, 58, 12, 4;
  0, 11978, 16169, 4116, 640, 68, 20, 4;
  ...
		

Links

• Scott R. Shannon, Image for n = 12.

Crossrefs

Cf. A359253 (regions), A359252 (vertices), A359254 (edges), A001859, A332723, A359061, A359009.

Formula

Sum of row n = A359253(n);