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

1,3

Comments

The infinite exterior region is not counted.

Links

Table of n, a(n) for n=1..13.

Scott R. Shannon, Image for a(3) = 37.

Scott R. Shannon, Image for a(4) = 245.

Scott R. Shannon, Image for a(5) = 1205.

Formula

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

Crossrefs

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

Sequence in context: A275750 A142445 A155974 * A190603 A142627 A142308

Adjacent sequences: A384699 A384700 A384701 * A384703 A384704 A384705

Keyword

nonn,more

Author

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

Status

approved