A384701 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 points where circles intersect.

2, 4, 18, 172, 978, 3672, 11034, 27241, 60804, 122741, 232138, 412263, 697058

Offset: 1

Author

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

Keywords

• nonn
• more

Links

• Scott R. Shannon, Image for a(2) = 4.
• Scott R. Shannon, Image for a(3) = 18.
• Scott R. Shannon, Image for a(4) = 172.
• Scott R. Shannon, Image for a(5) = 978.

Crossrefs

Cf. A384700 (circles), A384702 (regions), A384703 (edges), A359569, A374825, A374338, A373106.

Formula

a(n) = A384703(n) - A384702(n) + 1 by Euler's formula, for n > 1.