A360352
Number of regions among all distinct circles that can be constructed from an n X n square grid of points when each pair of points is connected by a circle and the points lie at the ends of a diameter of the circle.
Original entry on oeis.org
12, 168, 1536, 8904, 36880, 123468, 358036, 912776, 2105976
Offset: 2
- Scott R. Shannon, Image for n = 2. In this and other images the n X n grid points are shown as white dots.
- Scott R. Shannon, Image for n = 3.
- Scott R. Shannon, Image for n = 4.
- Scott R. Shannon, Image for n = 5.
- Scott R. Shannon, Image for n = 6.
- N. J. A. Sloane, New Gilbreath Conjectures, Sum and Erase, Dissecting Polygons, and Other New Sequences, Doron Zeilberger's Exper. Math. Seminar, Rutgers, Sep 14 2023: Video, Slides, Updates. (Mentions this sequence.)
A360354
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 when each pair of points is connected by a circle and the points lie at the ends of a diameter of the circle.
Original entry on oeis.org
8, 4, 40, 108, 20, 92, 904, 456, 76, 0, 8, 200, 4540, 3400, 652, 100, 4, 8, 404, 17244, 15324, 3148, 628, 116, 16, 528, 54252, 54476, 11672, 2152, 332, 44, 12, 972, 151992, 158468, 37244, 7940, 1120, 224, 48, 12, 16, 1404, 379488, 404148, 103436, 20216, 3316, 600, 132, 20, 16
Offset: 2
The table begins:
8, 4;
40, 108, 20;
92, 904, 456, 76, 0, 8;
200, 4540, 3400, 652, 100, 4, 8;
404, 17244, 15324, 3148, 628, 116, 16;
528, 54252, 54476, 11672, 2152, 332, 44, 12;
972, 151992, 158468, 37244, 7940, 1120, 224, 48, 12, 16;
1404, 379488, 404148, 103436, 20216, 3316, 600, 132, 20, 16;
1896, 868460, 923656, 252096, 49848, 7916, 1744, 276, 84;
.
.
A360350
Number of distinct circles that can be constructed from an n X n square grid of points when each pair of points is connected by a circle and the points lie at the ends of a diameter of the circle.
Original entry on oeis.org
5, 26, 79, 185, 366, 653, 1077, 1678, 2494, 3571, 4959, 6718, 8889, 11541, 14740, 18553, 23027, 28278, 34351, 41352, 49356, 58454, 68732, 80330, 93304, 107757, 123815, 141605, 161211, 182795, 206393, 232190, 260331, 290907, 324090, 360080, 398856, 440655, 485655
Offset: 2
- N. J. A. Sloane, New Gilbreath Conjectures, Sum and Erase, Dissecting Polygons, and Other New Sequences, Doron Zeilberger's Exper. Math. Seminar, Rutgers, Sep 14 2023: Video, Slides, Updates. (Mentions this sequence.)
-
a(n) = { my (p = vector(n^2, k, (k-1)%n + ((k-1)\n)*I)); #setbinop((i,j)->[i+j, norm(i-j)], p)-n^2; } \\ Rémy Sigrist, Sep 24 2023
A360353
Number of edges among all distinct circles that can be constructed from an n X n square grid of points when each pair of points is connected by a circle and the points lie at the ends of a diameter of the circle.
Original entry on oeis.org
16, 244, 2580, 15788, 67144, 227888, 668008, 1712960, 3968028
Offset: 2
A372614
Number of vertices among all distinct circles that can be constructed from the 3 vertices and the equally spaced 3*n points placed on the sides of an equilateral triangle, using only a compass.
Original entry on oeis.org
6, 87, 481, 1992, 6969, 15409, 35202, 58422, 107677, 159138, 268572, 350860, 557049
Offset: 0
A372731
Number of vertices among all distinct circles that can be constructed from the 3 vertices and the equally spaced 3*n points placed on the sides of an equilateral triangle when every pair of the 3 + 3*n points are connected by a circle and where the points lie at the ends of the circle's diameter.
Original entry on oeis.org
6, 51, 301, 1272, 3285, 8401, 16050, 30036, 49801, 80916, 120447, 180307, 249108, 350145, 465898, 618213
Offset: 0
A372977
Number of vertices among all distinct circles that can be constructed from the 4 vertices and the equally spaced 4*n points placed on the sides of a square, using only a compass.
Original entry on oeis.org
40, 553, 4204, 14505, 39004, 94365, 197464, 320925, 569600
Offset: 0
A373106
Number of vertices among all distinct circles that can be constructed from the 4 vertices and the equally spaced 4*n points placed on the sides of a square when every pair of the 4 + 4*n points are connected by a circle and where the points lie at the ends of the circle's diameter.
Original entry on oeis.org
5, 61, 677, 2533, 7705, 17269, 37161, 65089, 111877, 174545, 274213
Offset: 0
Showing 1-8 of 8 results.
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