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

1,3

Links

Table of n, a(n) for n=1..23.

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

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.

Crossrefs

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

Sequence in context: A001106 A023551 A022787 * A365190 A079770 A079771

Adjacent sequences: A384697 A384698 A384699 * A384701 A384702 A384703

Keyword

nonn,more

Author

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

Status

approved