A373110 Number of distinct circles that can be constructed from the 4 vertices and the equally spaced 4*n points placed on the sides of a square when every pair of the 4 + 4*n points are connected by a circle and where the points lie at the ends of the circle's diameter.

5, 22, 54, 99, 159, 232, 320, 421, 537, 666, 810, 967, 1139, 1324, 1524, 1737, 1965, 2206, 2462, 2731, 3015, 3312, 3624, 3949

Offset: 0

Author

Scott R. Shannon, May 25 2024

Keywords

• nonn
• more

Comments

A circle is constructed for every pair of the 4 + 4*n points, the two points lying at the ends of a diameter of the circle.

See A373106 and A373107 for images of the circles.

Crossrefs

Cf. A373106, A373107, A373108, A372981, A372735, A359931, A360350, A361622, A365669.

Formula

Conjectured:

For even n, a(n) = (14*n^2 + 21*n + 10)/2.

For odd n, a(n) = (14*n^2 + 21*n + 9)/2.