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

1,1

Links

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

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.

Formula

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

Crossrefs

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

Sequence in context: A213793 A287612 A308755 * A318394 A228933 A347514

Adjacent sequences: A384698 A384699 A384700 * A384702 A384703 A384704

Keyword

nonn,more

Author

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

Status

approved