A359862 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 a 2 x n square grid of points using only a compass.

3, 0, 16, 29, 0, 102, 117, 10, 2, 4, 368, 402, 64, 26, 1, 12, 860, 903, 252, 52, 0, 2, 12, 1812, 2028, 520, 110, 4, 3, 24, 3168, 3841, 960, 204, 8, 6, 32, 5420, 6804, 1748, 362, 24, 11, 44, 8388, 10987, 2826, 552, 46, 14, 56, 12808, 17122, 4448, 922, 72, 17, 64, 18348, 25257, 6594, 1370, 82, 26

Offset: 1

Author

Scott R. Shannon, Jan 16 2023

Keywords

• nonn
• tabf

Comments

See A359859 and A359860 for further details and images of the circles.

Examples

			The table begins:
   3;
   0,    16,    29;
   0,   102,   117,   10,    2;
   4,   368,   402,   64,   26,  1;
  12,   860,   903,  252,   52,  0,  2;
  12,  1812,  2028,  520,  110,  4,  3;
  24,  3168,  3841,  960,  204,  8,  6;
  32,  5420,  6804, 1748,  362, 24, 11;
  44,  8388, 10987, 2826,  552, 46, 14;
  56, 12808, 17122, 4448,  922, 72, 17;
  64, 18348, 25257, 6594, 1370, 82, 26;
  ...
		

Links

• Scott R. Shannon, Image for n = 7.

Crossrefs

Cf. A359859 (vertices), A359860 (regions), A359861 (edges), A001859, A359258.

Formula

Sum of row n = A359860(n).