A372733 Number of curved edges 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.

12, 138, 738, 2838, 7194, 17904, 33954, 62868, 103866, 167280, 248826, 370458, 511806, 715905, 952608, 1260366

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.

See A372731 and A372732 for images of the circles.

Links

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

Formula

a(n) = A372731(n) + A372732(n) - 1 by Euler's formula.

Crossrefs

Cf. A372731 (vertices), A372732 (regions), A372734 (k-gons), A372735 (number of circles), A372616, A371375, A356358, A360353.

Sequence in context: A216081 A264503 A000467 * A059517 A243966 A097167

Adjacent sequences: A372730 A372731 A372732 * A372734 A372735 A372736

Keyword

nonn,more

Author

Scott R. Shannon, May 12 2024

Status

approved