A372614 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

A372614

Number of vertices 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, using only a compass.

6, 87, 481, 1992, 6969, 15409, 35202, 58422, 107677, 159138, 268572, 350860, 557049

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

OFFSET

0,1

COMMENTS

A circle is constructed for every pair of the 3 + 3*n points, the first point defines the circle's center while the second the radius distance.

LINKS

Table of n, a(n) for n=0..12.

Scott R. Shannon, Image for n = 0. In this and other images the 3 + 3*n vertices forming the triangle 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.

Scott R. Shannon, Image for n = 4.

FORMULA

a(n) = A372616(n) - A372615(n) + 1 by Euler's formula.

CROSSREFS

Cf. A372615 (regions), A372616 (edges), A372617 (k-gons), A372682 (number of circles), A372731, A371373, A354605, A360351.

Sequence in context: A343636 A369624 A047786 * A181271 A249929 A289394

Adjacent sequences: A372611 A372612 A372613 * A372615 A372616 A372617

KEYWORD

nonn,more

AUTHOR

Scott R. Shannon, May 07 2024

STATUS

approved