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.

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

Author

Scott R. Shannon, Feb 03 2023

Keywords

• nonn

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.)

Crossrefs

Cf. A360351 (vertices), A360352 (regions), A360353 (edges), A360354 (k-gons), A359931.

Programs

PARI

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

Extensions

More terms from Rémy Sigrist, Sep 24 2023