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A372615
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, using only a compass.
8
7, 121, 624, 2368, 7912, 17115, 38461, 63184, 115614, 170149, 285715, 371982, 588043
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.
The vertices of the initial equilateral triangle are indicated by small circles in the illustrations here.
LINKS
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) = A372616(n) - A372614(n) + 1 by Euler's formula.
CROSSREFS
Cf. A372614 (vertices), A372616 (edges), A372617 (k-gons), A372682 (number of circles), A371374, A353782, A360352.
Sequence in context: A196583 A197041 A283625 * A095752 A113267 A274267
KEYWORD
nonn,more
AUTHOR
Scott R. Shannon, May 07 2024
STATUS
approved