A385161 Place a point on the integer coordinates, up to |n|, along all four axial directions on a Cartesian plane, and then join a circle through every unordered triple of non-collinear points: a(n) is the number of distinct (finite) regions created.

1, 117, 4713, 41173, 233365, 725081, 2323869

Offset: 1

Author

Scott R. Shannon, Jul 10 2025

Keywords

• nonn
• more

Links

• Scott R. Shannon, Image for n = 2. The 4 x 2 = 8 starting points are shown as white dots.
• Scott R. Shannon, Image for n = 3. The 4 x 3 = 12 starting points are shown as white dots.

Crossrefs

Cf. A385159 (total circles), A385160 (vertices), A385162 (edges), A384702, A374826, A372977, A359570.

Formula

a(n) = A385162(n) - A385160(n) + 1 by Euler's formula.