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A359933
Number of regions among all distinct circles that can be constructed from an n X n square grid of points using only a compass.
8
45, 836, 8197, 43252, 167157, 535572
OFFSET
2,1
COMMENTS
A circle is constructed for every pair of the n X n points; the first point defines the circle's center while the second defines the radius. The number of distinct circles constructed from the n X n points is A359931(n).
No formula for a(n) is known.
LINKS
Scott R. Shannon, Image for n = 2. In this and other images the n X n grid points are shown as white dots.
Scott R. Shannon, Image for n = 3.
Scott R. Shannon, Image for n = 4.
Scott R. Shannon, Image for n = 5.
FORMULA
a(n) = A359934(n) - A359932(n) + 1 by Euler's formula.
CROSSREFS
Cf. A359932 (vertices), A359934 (edges), A359935 (k-gons), A359931 (distinct circles), A359860, A359253.
Sequence in context: A341427 A024379 A134290 * A341573 A078761 A034967
KEYWORD
nonn,more
AUTHOR
Scott R. Shannon, Jan 21 2023
STATUS
approved