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

1,2

Comments

The edges being counted are of course arcs of circles.

Links

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

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

Formula

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

Crossrefs

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

Sequence in context: A156469 A001545 A208954 * A269507 A302942 A292305

Adjacent sequences: A384700 A384701 A384702 * A384704 A384705 A384706

Keyword

nonn,more

Author

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

Status

approved