A373107 Number of regions 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.

12, 136, 932, 3252, 9144, 20032, 41260, 71832, 121460, 188656, 291488

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 as white dots for clarity.

Scott R. Shannon, Image for n = 1.

Scott R. Shannon, Image for n = 2.

Scott R. Shannon, Image for n = 3.

Scott R. Shannon, Image for n = 7.

Formula

a(n) = A373108(n) - A373106(n) + 1 by Euler's formula.

Crossrefs

Cf. A373106 (vertices), A373108 (edges), A373109 (k-gons), A373110 (circles), A372978, A372732, A358782, A362234, A360352.

Sequence in context: A030023 A194013 A189501 * A351514 A216081 A264503

Adjacent sequences: A373104 A373105 A373106 * A373108 A373109 A373110

Keyword

nonn,more

Author

Scott R. Shannon, May 25 2024

Status

approved