A354605
Number of vertices among all distinct circles that can be constructed from a point on the origin and n equally spaced points on each of the +x,-x,+y,-y coordinates axes using only a compass.
Original entry on oeis.org
101, 1145, 5001, 13753, 34497, 72185, 135157, 224321
Offset: 1
A359932
Number of vertices among all distinct circles that can be constructed from an n x n square grid of points using only a compass.
Original entry on oeis.org
40, 689, 7240, 38729, 151584, 488741
Offset: 2
A359860
Number of regions among all distinct circles that can be constructed from a 2 X n square grid of points using only a compass.
Original entry on oeis.org
3, 45, 231, 865, 2081, 4489, 8211, 14401, 22857, 35445, 51741, 74397, 102271, 138801, 182739, 238181, 303175, 383097, 474995, 586021, 712003, 860829, 1028225, 1223773, 1440593, 1689993, 1965525, 2279509, 2622993, 3011405, 3433615, 3907241, 4419261, 4988781, 5603271
Offset: 1
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.
Original entry on oeis.org
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
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;
...
A359861
Number of edges among all distinct circles that can be constructed from a 2 X n square grid of points using only a compass.
Original entry on oeis.org
4, 84, 420, 1604, 3904, 8444, 15524, 27356, 43540, 67720, 99088, 142912, 196820, 267580, 352844, 460432, 586592, 741852, 920528, 1136888, 1382360, 1672384, 1998964, 2380940, 2804292, 3291376, 3830048, 4444176, 5116128, 5876580, 6703220, 7631352, 8634796, 9751064, 10956320
Offset: 1
a(n) = A359859(n) + A359860(n) - 1 by Euler's formula.
Showing 1-5 of 5 results.
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