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 A119437 Table T(n,k) = number of lines through exactly k points of an n X n grid of points. 5
 6, 12, 8, 48, 4, 10, 108, 16, 4, 12, 248, 36, 4, 4, 14, 428, 64, 20, 4, 4, 16, 764, 100, 44, 4, 4, 4, 18, 1196, 204, 36, 24, 4, 4, 4, 20, 1900, 252, 64, 52, 4, 4, 4, 4, 22, 2668, 396, 124, 40, 28, 4, 4, 4, 4, 24, 3824, 572, 200, 20, 60, 4, 4, 4, 4, 4, 26, 5244, 780, 236, 76, 44, 32 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 LINKS Seiichi Manyama, Rows n = 2..141, flattened S. Mustonen, On lines and their intersection points in a rectangular grid of points [From Seppo Mustonen, Apr 18 2009] Seppo Mustonen, On lines and their intersection points in a rectangular grid of points [Local copy] FORMULA T(n,k) = 1/2 (f(n, k+1) - 2 f(n, k) + f(n, k-1)) where f(n, k) = Sum_{-n < kx < n, -n < ky < n, gcd(x, y)=1} (n - |kx|)*(n - |ky|). [Seppo Mustonen, Apr 18 2009] EXAMPLE From Seiichi Manyama, Nov 26 2017: (Start) The table starts: n\k| 2 3 4 5 6 7 8 ---+------------------------------ 2 | 6; 3 | 12, 8; 4 | 48, 4, 10; 5 | 108 16, 4, 12; 6 | 248, 36, 4, 4, 14; 7 | 428, 64, 20, 4, 4, 16; 8 | 764, 100, 44, 4, 4, 4, 18; (End) CROSSREFS Row sums A018808; columns A018809-A018817. See A119439 for another version. Sequence in context: A162522 A292680 A028320 * A243033 A242549 A315777 Adjacent sequences: A119434 A119435 A119436 * A119438 A119439 A119440 KEYWORD nonn,tabl AUTHOR Franklin T. Adams-Watters, May 19 2006 EXTENSIONS An incorrect formula removed by Seppo Mustonen, Apr 25 2009 STATUS approved

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Last modified February 29 09:21 EST 2024. Contains 370418 sequences. (Running on oeis4.)