A358746 The number of vertices 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, 6, 5, 55, 54, 252, 169, 747, 630, 1804, 1381, 3679, 3150, 6690, 5553, 11509, 9846, 18012, 15241, 27237, 24398, 39606, 33577, 56275, 50622, 77058, 69693, 102979, 94770, 135966, 124065, 175593, 162894, 222810, 205885, 279831, 260870, 347178, 321961, 424391, 399042

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.

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.

Scott R. Shannon, Image for n = 10.

Scott R. Shannon, Image for n = 16.

Scott R. Shannon, Image for n = 17.

Formula

a(n) = A358783(n) - A358782(n) + 1 by Euler's formula.

Crossrefs

Cf. A358782 (regions), A358783 (edges), A359009 (k-gons), A007569, A146212.

See allso A370976-A370979.

Sequence in context: A280462 A283475 A343995 * A175350 A085057 A069113

Adjacent sequences: A358743 A358744 A358745 * A358747 A358748 A358749

Keyword

nonn

Author

Scott R. Shannon, Nov 30 2022

Status

approved