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 A372734 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 the 3 vertices and the equally spaced 3*n points placed on the sides of an equilateral triangle when every pair of the 3 + 3*n points are connected by a circle and where the points lie at the ends of the circle's diameter. 4
 0, 7, 12, 61, 9, 6, 6, 303, 108, 9, 9, 3, 18, 771, 603, 150, 15, 9, 0, 1, 24, 1722, 1740, 339, 81, 3, 0, 1, 30, 3789, 4326, 1104, 234, 18, 3, 36, 6907, 8274, 2193, 432, 45, 18, 66, 12012, 15504, 4173, 922, 105, 45, 3, 3, 90, 19860, 24774, 7389, 1773, 150, 30, 48, 30594, 39852, 12438, 2998, 387, 48 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS A circle is constructed for every pair of the 3 + 3*n points, the two points lying at the ends of a diameter of the circle. See A372731 and A372732 for images of the circles. LINKS Table of n, a(n) for n=0..64. FORMULA Sum of row(n) = A372732(n). EXAMPLE The table begins: 0, 7; 12, 61, 9, 6; 6, 303, 108, 9, 9, 3; 18, 771, 603, 150, 15, 9, 0, 1; 24, 1722, 1740, 339, 81, 3, 0, 1; 30, 3789, 4326, 1104, 234, 18, 3; 36, 6907, 8274, 2193, 432, 45, 18; 66, 12012, 15504, 4173, 922, 105, 45, 3, 3; 90, 19860, 24774, 7389, 1773, 150, 30; 48, 30594, 39852, 12438, 2998, 387, 48; 96, 45456, 59019, 18669, 4429, 609, 93, 3, 6; 90, 66633, 86088, 29136, 6840, 1164, 195, 6; 120, 90210, 121614, 40035, 9160, 1362, 177, 12, 9; 108, 124245, 167646, 57048, 14377, 1989, 300, 33, 15; . . CROSSREFS Cf. A372731 (vertices), A372732 (regions), A372733 (edges), A372735 (number of circles), A372617, A371376, A361623, A360354. Sequence in context: A038278 A266056 A083335 * A358782 A119179 A121983 Adjacent sequences: A372731 A372732 A372733 * A372735 A372736 A372737 KEYWORD nonn,tabf AUTHOR Scott R. Shannon, May 12 2024 STATUS approved

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Last modified August 6 14:07 EDT 2024. Contains 374974 sequences. (Running on oeis4.)