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

2,1

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

Links

Table of n, a(n) for n=2..42.

Formula

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

Crossrefs

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

See allso A370976-A370979.

Sequence in context: A274890 A327570 A057123 * A134833 A057827 A266802

Adjacent sequences: A358780 A358781 A358782 * A358784 A358785 A358786

Keyword

nonn

Author

Scott R. Shannon, Nov 30 2022

Status

approved