A358782 - OEIS

A358782

The number of regions 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.

1, 7, 12, 66, 85, 281, 264, 802, 821, 1893, 1740, 3810, 3725, 6871, 6448, 11748, 11125, 18317, 17160, 27616, 26797, 40067, 37176, 56826, 54653, 77707, 74788, 103734, 101041, 136835, 131744, 176584, 172109, 223931, 216900, 281090, 273829, 348583, 337480, 425950, 416641

(list; graph; refs; listen; history; text; internal format)

OFFSET

2,2

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.

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.

Scott R. Shannon, Image for n = 2. In this and other images the points defining the circle diameters are show as white dots.

Scott R. Shannon, Image for n = 3.

Scott R. Shannon, Image for n = 4.

Scott R. Shannon, Image for n = 5.

Scott R. Shannon, Image for n = 6.

Scott R. Shannon, Image for n = 7.

Scott R. Shannon, Image for n = 8.

Scott R. Shannon, Image for n = 9.