A372731 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 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.

6, 51, 301, 1272, 3285, 8401, 16050, 30036, 49801, 80916, 120447, 180307, 249108, 350145, 465898, 618213

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. 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) = A372733(n) - A372732(n) + 1 by Euler's formula.

Crossrefs

Cf. A372732 (regions), A372733 (edges), A372734 (k-gons), A372735 (number of circles), A372614, A371373, A354605, A360351.

Sequence in context: A372336 A133395 A341424 * A050916 A376568 A011790

Adjacent sequences: A372728 A372729 A372730 * A372732 A372733 A372734

Keyword

nonn,more

Author

Scott R. Shannon, May 12 2024

Status

approved