A384703 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 edges in the planar graph formed from the intersections of the circles.

0, 4, 54, 416, 2182, 7884, 23294, 56982, 126310, 253564, 477462, 844524, 1424316

Offset: 1

Author

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

Keywords

• nonn
• more

Comments

The edges being counted are of course arcs of circles.

Links

• Scott R. Shannon, Image for a(3) = 54.

Crossrefs

Cf. A384700 (circles), A384701 (vertices), A384702 (regions), A359571, A374827, A374339, A373108.

Formula

a(n) = A384701(n) + A384702(n) - 1 by Euler's formula, for n > 1.