A372732 Number of regions among all distinct circles that can be constructed from the 3 vertices and the equally spaced 3*n points placed on the sides of an equilateral triangle when every pair of the 3 + 3*n points are connected by a circle and where the points lie at the ends of the circle's diameter.

7, 88, 438, 1567, 3910, 9504, 17905, 32833, 54066, 86365, 128380, 190152, 262699, 365761, 486711, 642154

Offset

0,1

Comments

A circle is constructed for every pair of the 3 + 3*n points, the two points lying at the ends of a diameter of the circle.

Links

Table of n, a(n) for n=0..15.

Scott R. Shannon, Image for n = 0.

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 = 4.

Formula

a(n) = A372733(n) - A372731(n) + 1 by Euler's formula.

Crossrefs

Cf. A372731 (vertices), A372733 (edges), A372734 (k-gons), A372735 (number of circles), A372615, A371374, A353782, A360352.

Sequence in context: A132486 A297547 A183486 * A155465 A296735 A137143

Adjacent sequences: A372729 A372730 A372731 * A372733 A372734 A372735

Keyword

nonn,more

Author

Scott R. Shannon, May 12 2024

Status

approved