A385160 Place a point on the integer coordinates, up to |n|, along all four axial directions on a Cartesian plane, and then join a circle through every unordered triple of non-collinear points: a(n) is the number of distinct points where circles intersect.

4, 68, 4244, 38100, 222300, 695544, 2252764

Offset

1,1

Links

Table of n, a(n) for n=1..7.

Scott R. Shannon, Image for n = 2. The 4 x 2 = 8 starting points are shown as white dots.

Scott R. Shannon, Image for n = 3. The 4 x 3 = 12 starting points are shown as white dots.

Formula

a(n) = A385162(n) - A385161(n) + 1 by Euler's formula.

Crossrefs

Cf. A385159 (total circles), A385161 (regions), A385162 (edges), A384703, A383461, A374825, A359569.

Sequence in context: A009791 A012484 A174809 * A363427 A125587 A134794

Adjacent sequences: A385157 A385158 A385159 * A385161 A385162 A385163

Keyword

nonn,more

Author

Scott R. Shannon, Jul 10 2025

Status

approved