A384702 On a 2 X n grid of vertices, draw a circle through every unordered triple of non-collinear vertices: a(n) is the number of distinct (finite) regions created.

0, 1, 37, 245, 1205, 4213, 12261, 29742, 65507, 130824, 245325, 432262, 727259

Offset: 1

Author

Scott R. Shannon and N. J. A. Sloane, Jun 07 2025

Keywords

• nonn
• more

Comments

The infinite exterior region is not counted.

Links

• Scott R. Shannon, Image for a(3) = 37.
• Scott R. Shannon, Image for a(4) = 245.
• Scott R. Shannon, Image for a(5) = 1205.

Crossrefs

Cf. A384700 (circles), A384701 (vertices), A384703 (edges), A359570, A374826, A374337, A372978.

Formula

a(n) = A384703(n) - A384701(n) + 1 by Euler's formula, for n > 1.