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A354605
Number of vertices among all distinct circles that can be constructed from a point on the origin and n equally spaced points on each of the +x,-x,+y,-y coordinates axes using only a compass.
9
101, 1145, 5001, 13753, 34497, 72185, 135157, 224321
OFFSET
1,1
COMMENTS
A circle is constructed for every pair of the 1 + 4n points, the first point defines the circle's center while the second the radius distance. The number of distinct circles constructed from the points is A361622(n).
No formula for a(n) is currently known.
LINKS
Scott R. Shannon, Image for n = 1.
Scott R. Shannon, Image for n = 2.
Scott R. Shannon, Image for n = 3.
FORMULA
a(n) = A356358 - A353782(n) + 1 by Euler's formula.
CROSSREFS
Cf. A353782 (regions), A356358 (edges), A361623 (k-gons), A361622 (distinct circles), A359932, A359859, A359252, A359569, A331702.
Sequence in context: A290827 A290835 A290549 * A275986 A368416 A215119
KEYWORD
nonn,more
AUTHOR
Scott R. Shannon, Mar 13 2023
STATUS
approved