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 A359935 Irregular table read by rows: T(n,k) is the number of k-gons, k>=2, among all distinct circles that can be constructed from an n x n square grid of points using only a compass. 8
 0, 16, 30, 0, 412, 341, 60, 20, 4, 0, 3464, 3534, 928, 212, 48, 12, 0, 16936, 19861, 5252, 1056, 88, 52, 8, 0, 63712, 77394, 20480, 4820, 612, 108, 20, 12, 4, 202904, 244013, 71244, 14968, 1852, 472, 80, 32, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 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 the radius distance. The number of distinct circles constructed from the n x n points is A359931(n). See A359932 and A359933 for images of the circles. The first occurrence of a 2-gon is when n = 7. Assuming the grid points are separated by 1 unit, in the first quadrant this region has endpoints (6,7) and (7,6) - an equivalent region is in each of the three other quadrants. Its arcs are from two circles, one with center at (2,2) going through point (-2,-3) while the other has center (3,3) going through point (0,-1). See the attached image. LINKS Table of n, a(n) for n=2..44. Scott R. Shannon, Close-up of the circles for n = 7. The 2-gon is the thin region shown in white in the upper-right corner. FORMULA Sum of row n = A359933(n). EXAMPLE The table begins: 0, 16, 30; 0, 412, 341, 60, 20, 4; 0, 3464, 3534, 928, 212, 48, 12; 0, 16936, 19861, 5252, 1056, 88, 52, 8; 0, 63712, 77394, 20480, 4820, 612, 108, 20, 12; 4, 202904, 244013, 71244, 14968, 1852, 472, 80, 32, 4; . . CROSSREFS Cf. A359932 (vertices), A359933 (regions), A359934 (edges), A359931 (distinct circles), A359862, A359258. Sequence in context: A115278 A372980 A228664 * A217715 A064634 A255265 Adjacent sequences: A359932 A359933 A359934 * A359936 A359937 A359938 KEYWORD nonn,tabf,more AUTHOR Scott R. Shannon, Jan 21 2023 STATUS approved

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Last modified September 15 02:41 EDT 2024. Contains 375930 sequences. (Running on oeis4.)