A358783 The number of edges formed when every pair of n points, placed at the vertices of a regular n-gon, are connected by a circle and where the points lie at the ends of the circle's diameter.

2, 12, 16, 120, 138, 532, 432, 1548, 1450, 3696, 3120, 7488, 6874, 13560, 12000, 23256, 20970, 36328, 32400, 54852, 51194, 79672, 70752, 113100, 105274, 154764, 144480, 206712, 195810, 272800, 255808, 352176, 335002, 446740, 422784, 560920, 534698, 695760, 659440, 850340, 815682

Offset: 2

Author

Scott R. Shannon, Nov 30 2022

Keywords

• nonn

Comments

Conjecture: for odd values of n all vertices are simple, other than those defining the diameters of the circles. No formula for n, or only the odd values of n, is currently known.

See A358746 and A358782 for images of the circles.

The author thanks Zach Shannon some of whose code was used in the generation of this sequence.

If n is odd, the circle containing the initial n points is not part of the graph (compare A370976-A370979). - N. J. A. Sloane, Mar 25 2024

Crossrefs

Cf. A358746 (vertices), A358782 (regions), A359009 (k-gons), A135565, A344899.

See allso A370976-A370979.

Formula

a(n) = A358746(n) + A358782(n) - 1 by Euler's formula.