A373106 Number of vertices among all 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, 61, 677, 2533, 7705, 17269, 37161, 65089, 111877, 174545, 274213

Offset

0,1

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.

Links

Table of n, a(n) for n=0..10.

Scott R. Shannon, Image for n = 0. In this and other images the 4 + 4*n vertices forming the square are drawn larger for clarity.

Scott R. Shannon, Image for n = 1.

Scott R. Shannon, Image for n = 2.

Scott R. Shannon, Image for n = 3.

Formula

a(n) = A373108(n) - A373107(n) + 1 by Euler's formula.

Crossrefs

Cf. A373107 (regions), A373108 (edges), A373109 (k-gons), A373110 (circles), A372977, A372731, A358746, A362233, A360351.

Sequence in context: A099666 A350973 A189444 * A217811 A217280 A236955

Adjacent sequences: A373103 A373104 A373105 * A373107 A373108 A373109

Keyword

nonn,more

Author

Scott R. Shannon, May 25 2024

Status

approved