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%I #22 Mar 13 2020 19:51:19
%S 6,12,8,48,4,10,108,16,4,12,248,36,4,4,14,428,64,20,4,4,16,764,100,44,
%T 4,4,4,18,1196,204,36,24,4,4,4,20,1900,252,64,52,4,4,4,4,22,2668,396,
%U 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
%N Table T(n,k) = number of lines through exactly k points of an n X n grid of points.
%H Seiichi Manyama, <a href="/A119437/b119437.txt">Rows n = 2..141, flattened</a>
%H S. Mustonen, <a href="http://www.survo.fi/papers/PointsInGrid.pdf">On lines and their intersection points in a rectangular grid of points</a> [From _Seppo Mustonen_, Apr 18 2009]
%H Seppo Mustonen, <a href="/A018808/a018808.pdf">On lines and their intersection points in a rectangular grid of points</a> [Local copy]
%F 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]
%e From _Seiichi Manyama_, Nov 26 2017: (Start)
%e The table starts:
%e n\k| 2 3 4 5 6 7 8
%e ---+------------------------------
%e 2 | 6;
%e 3 | 12, 8;
%e 4 | 48, 4, 10;
%e 5 | 108 16, 4, 12;
%e 6 | 248, 36, 4, 4, 14;
%e 7 | 428, 64, 20, 4, 4, 16;
%e 8 | 764, 100, 44, 4, 4, 4, 18; (End)
%Y Row sums A018808; columns A018809-A018817. See A119439 for another version.
%K nonn,tabl
%O 2,1
%A _Franklin T. Adams-Watters_, May 19 2006
%E An incorrect formula removed by _Seppo Mustonen_, Apr 25 2009
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