A384700 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 circles created.

0, 1, 9, 24, 52, 93, 153, 232, 336, 465, 625, 816, 1044, 1309, 1617, 1968, 2368, 2817, 3321, 3880, 4500, 5181, 5929

Offset: 1

Author

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

Keywords

• nonn
• more

Links

• Scott R. Shannon, Image for a(3) = 9.

Crossrefs

Cf. A384701 (vertices), A384702 (regions), A384703 (edges), A365669, A374338, A373110, A372981,

Formula

Conjecture:

for even n, a(n) = n^3/2 - n^2/4 - n,

for odd n > 1, a(n) = n^3/2 - n^2/4 - n + 3/4.