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%I #4 Mar 31 2012 13:21:31
%S 1,1,1,1,4,6,1,9,12,8,1,16,48,4,10,1,25,108,16,4,12,1,36,248,36,4,4,
%T 14,1,49,428,64,20,4,4,16,1,64,764,100,44,4,4,4,18,1,81,1196,204,36,
%U 24,4,4,4,20,1,100,1900,252,64,52,4,4,4,4,22,1,121,2668,396,124,40,28,4,4,4,4
%N Triangle T(n,k) = number of sets of m points determined by the intersection of a line with an n X n grid of points.
%C Each singleton point is determined by all but finitely many of the family of lines passing through that point and the empty set is determined by any randomly positioned line.
%F T(n,0) = 1, T(n,1) = n^2, T(n,k) = A119437(n,k) for k>1.
%e The table starts:
%e 1,
%e 1,1,
%e 1,4,6,
%e 1,9,12,8,
%e 1,16,48,4,10,
%Y Row sums A119438; columns A000290, A018809-A018817. See A119437 for another version.
%K nonn,tabl
%O 0,5
%A _Franklin T. Adams-Watters_, May 19 2006