

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.


8



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
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OFFSET

2,1


COMMENTS

A circle is constructed for every pair of points on the n X n grid, the points lying at the ends of a diameter of the circle.
No formula for a(n) is known.
See A360351 and A360352 for images of the resulting vertices and regions.


LINKS

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.)


PROG

(PARI) a(n) = { my (p = vector(n^2, k, (k1)%n + ((k1)\n)*I)); #setbinop((i, j)>[i+j, norm(ij)], p)n^2; } \\ Rémy Sigrist, Sep 24 2023


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



