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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.
8
6, 87, 481, 1992, 6969, 15409, 35202, 58422, 107677, 159138, 268572, 350860, 557049
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
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
KEYWORD
nonn,more
AUTHOR
Scott R. Shannon, May 07 2024
STATUS
approved