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A372978
Number of regions among all distinct circles that can be constructed from the 4 vertices and the equally spaced 4*n points placed on the sides of a square, using only a compass.
6
45, 628, 4633, 15476, 41561, 98808, 206317, 333272, 590181
OFFSET
0,1
COMMENTS
A circle is constructed for every pair of the 4 + 4*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 4 + 4*n vertices forming the square are drawn as white dots for clarity.
Scott R. Shannon, Image for n = 1.
Scott R. Shannon, Image for n = 2.
Scott R. Shannon, Image for n = 3.
FORMULA
a(n) = A372979(n) - A372977(n) + 1 by Euler's formula.
CROSSREFS
Cf. A372977 (vertices), A372979 (edges), A372980 (k-gons), A372981 (circles), A372615, A371374, A353782, A360352.
Sequence in context: A189350 A090024 A282767 * A160234 A110691 A296540
KEYWORD
nonn,more
AUTHOR
Scott R. Shannon, May 19 2024
STATUS
approved