A359932 Number of vertices among all distinct circles that can be constructed from an n x n square grid of points using only a compass.

40, 689, 7240, 38729, 151584, 488741

Offset: 2

Author

Scott R. Shannon, Jan 19 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 the radius distance. 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.
• Scott R. Shannon, Image for n = 3.
• Scott R. Shannon, Image for n = 4.

Crossrefs

Cf. A359933 (regions), A359934 (edges), A359935 (k-gons), A359931 (distinct circles), A359859, A359252.

Formula

a(n) = A359934(n) - A359933(n) + 1 by Euler's formula.