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A360350 Number of 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. 8
5, 26, 79, 185, 366, 653, 1077, 1678, 2494, 3571, 4959, 6718, 8889, 11541, 14740, 18553, 23027, 28278, 34351, 41352, 49356, 58454, 68732, 80330, 93304, 107757, 123815, 141605, 161211, 182795, 206393, 232190, 260331, 290907, 324090, 360080, 398856, 440655, 485655 (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.
No formula for a(n) is known.
See A360351 and A360352 for images of the resulting vertices and regions.
LINKS
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.)
PROG
(PARI) a(n) = { my (p = vector(n^2, k, (k-1)%n + ((k-1)\n)*I)); #setbinop((i, j)->[i+j, norm(i-j)], p)-n^2; } \\ Rémy Sigrist, Sep 24 2023
CROSSREFS
Cf. A360351 (vertices), A360352 (regions), A360353 (edges), A360354 (k-gons), A359931.
Sequence in context: A081886 A081530 A254831 * A145013 A096943 A166810
KEYWORD
nonn
AUTHOR
Scott R. Shannon, Feb 03 2023
EXTENSIONS
More terms from Rémy Sigrist, Sep 24 2023
STATUS
approved

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Last modified July 22 12:38 EDT 2024. Contains 374499 sequences. (Running on oeis4.)