A359935
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 an n x n square grid of points using only a compass.
Original entry on oeis.org
0, 16, 30, 0, 412, 341, 60, 20, 4, 0, 3464, 3534, 928, 212, 48, 12, 0, 16936, 19861, 5252, 1056, 88, 52, 8, 0, 63712, 77394, 20480, 4820, 612, 108, 20, 12, 4, 202904, 244013, 71244, 14968, 1852, 472, 80, 32, 4
Offset: 2
The table begins:
0, 16, 30;
0, 412, 341, 60, 20, 4;
0, 3464, 3534, 928, 212, 48, 12;
0, 16936, 19861, 5252, 1056, 88, 52, 8;
0, 63712, 77394, 20480, 4820, 612, 108, 20, 12;
4, 202904, 244013, 71244, 14968, 1852, 472, 80, 32, 4;
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A361623
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 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
0, 40, 60, 12, 0, 484, 583, 160, 28, 8, 0, 2196, 2416, 804, 104, 28, 0, 5676, 6616, 2184, 460, 40, 8, 13456, 16936, 5236, 1340, 104, 12, 4, 27512, 35032, 11796, 2400, 320, 28, 0, 4, 0, 50688, 65044, 22536, 4632, 584, 60, 12, 4, 8, 84300, 105860, 38024, 8124, 1080, 108
Offset: 1
The table begins:
0, 40, 60, 12;
0, 484, 583, 160, 28, 8;
0, 2196, 2416, 804, 104, 28;
0, 5676, 6616, 2184, 460, 40;
8, 13456, 16936, 5236, 1340, 104, 12;
4, 27512, 35032, 11796, 2400, 320, 28, 0, 4;
0, 50688, 65044, 22536, 4632, 584, 60, 12, 4;
8, 84300, 105860, 38024, 8124, 1080, 108;
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A359859
Number of vertices 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
2, 40, 190, 740, 1824, 3956, 7314, 12956, 20684, 32276, 47348, 68516, 94550, 128780, 170106, 222252, 283418, 358756, 445534, 550868, 670358, 811556, 970740, 1157168, 1363700, 1601384, 1864524, 2164668, 2493136, 2865176, 3269606, 3724112, 4215536, 4762284, 5353050
Offset: 1
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
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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