A359933 Number of regions among all distinct circles that can be constructed from an n X n square grid of points using only a compass.

45, 836, 8197, 43252, 167157, 535572

Offset: 2

Author

Scott R. Shannon, Jan 21 2023

Keywords

• nonn
• more

Comments

A circle is constructed for every pair of the n X n points; the first point defines the circle's center while the second defines the radius. The number of distinct circles constructed from the n X n points is A359931(n).

No formula for a(n) is known.

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.

Crossrefs

Cf. A359932 (vertices), A359934 (edges), A359935 (k-gons), A359931 (distinct circles), A359860, A359253.

Formula

a(n) = A359934(n) - A359932(n) + 1 by Euler's formula.