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A360352 Number of regions among all distinct circles that can be constructed from an n X n square grid of points when each pair of points is connected by a circle and the points lie at the ends of a diameter of the circle. 9
12, 168, 1536, 8904, 36880, 123468, 358036, 912776, 2105976 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,1
COMMENTS
A circle is constructed for every pair of points on the n X n grid, the points lying at the ends of a diameter of the circle. The number of distinct circles constructed from the n X n grid is A360350(n).
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.
Scott R. Shannon, Image for n = 6.
N. J. A. Sloane, New Gilbreath Conjectures, Sum and Erase, Dissecting Polygons, and Other New Sequences, Doron Zeilberger's Exper. Math. Seminar, Rutgers, Sep 14 2023: Video, Slides, Updates. (Mentions this sequence.)
FORMULA
a(n) = A360353(n) - A360351(n) + 1 by Euler's formula.
CROSSREFS
Cf. A360351 (vertices), A360353 (edges), A360354 (k-gons), A360350 (distinct circles), A359933.
Sequence in context: A160566 A324414 A099745 * A268899 A366710 A182606
KEYWORD
nonn,more
AUTHOR
Scott R. Shannon, Feb 04 2023
STATUS
approved

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Last modified July 18 09:18 EDT 2024. Contains 374378 sequences. (Running on oeis4.)