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 A222591 Numerators of (n*(n - 3)/6) + 1, arising as the maximum possible number of triple lines for an n-element set. 0
 1, 5, 8, 4, 17, 23, 10, 38, 47, 19, 68, 80, 31, 107, 122, 46, 155, 173, 64, 212, 233, 85, 278, 302, 109, 353, 380, 136, 437, 467, 166, 530, 563, 199, 632, 668, 235, 743, 782, 274, 863, 905, 316, 992, 1037, 361, 1130, 1178, 409, 1277, 1328 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,2 COMMENTS Numerators of (n*(n - 3)/6) + 1, which arises as the maximum possible number of triple lines for an n-element set, according to Green and Tao, cited in Elekes. The fractions for n = 3, 4, 5, 6, ... are 1/1, 5/3, 8/3, 4/1, 17/3, 23/3, 10/1, 38/3, 47/3, 19/1, 68/3, 80/3, 31/1, 107/3, 122/3, 46/1, 155/3, 173/3, 64/1, 212/3, 233/3, 85/1, 278/3, 302/3, 109/1, 353/3, 380/3, 136/1, 437/3, 467/3, 166/1, 530/3, 563/3, 199/1, 632/3, 668/3, 235/1, 743/3, 782/3, 274/1, 863/3, 905/3, 316/1, 992/3, 1037/3, 361/1, 1130/3, 1178/3, 409/1, 1277/3, 1328/3. The corresponding denominators are A169609. LINKS Table of n, a(n) for n=3..53. György Elekes, Endre Szabó, On Triple Lines and Cubic Curves --- the Orchard Problem revisited, arXiv:1302.5777 [math.CO], Feb 23, 2013. Index entries for linear recurrences with constant coefficients, signature (0,0,3,0,0,-3,0,0,1). EXAMPLE a(10) = 38 because (10*(10 - 3)/6) + 1 = 38/3. MATHEMATICA Numerator[Table[(n(n-3))/6+1, {n, 3, 60}]] (* or *) LinearRecurrence[{0, 0, 3, 0, 0, -3, 0, 0, 1}, {1, 5, 8, 4, 17, 23, 10, 38, 47}, 60] (* Harvey P. Dale, Feb 11 2015 *) CROSSREFS Cf. A169609. Sequence in context: A020857 A096413 A334116 * A299447 A300085 A186691 Adjacent sequences: A222588 A222589 A222590 * A222592 A222593 A222594 KEYWORD nonn,easy,frac AUTHOR Jonathan Vos Post, Feb 25 2013 STATUS approved

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Last modified May 30 17:43 EDT 2024. Contains 372971 sequences. (Running on oeis4.)