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.

12, 168, 1536, 8904, 36880, 123468, 358036, 912776, 2105976

Offset: 2

Author

Scott R. Shannon, Feb 04 2023

Keywords

• nonn
• more

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. The number of distinct circles constructed from the n X n grid is A360350(n).

Links

• 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.)

Crossrefs

Cf. A360351 (vertices), A360353 (edges), A360354 (k-gons), A360350 (distinct circles), A359933.

Formula

a(n) = A360353(n) - A360351(n) + 1 by Euler's formula.