%I #9 Apr 10 2021 08:04:17
%S 1,2,0,2,1,0,1,2,1,0,1,1,2,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,0,2,1,1,1,1,
%T 1,1,0,2,2,1,0,1,1,1,1,0,2,2,0,2,1,0,1,1,1,0,2,0,2,2,0,2,1,0,1,1,0,2,
%U 0,2,1,1,2,0,2,0,1,1,0,2,0,2,0,2,0,2,0,2,1,1,1,0,2,0,2,0,2,0,2
%N Triangular array: g(n,k) = number of fractional parts (i*Pi) in interval [(k-1)/n, k/n], for 1 <= i <= n, 1 <= k <= n.
%C See A194285.
%e First eleven rows:
%e 1;
%e 2, 0;
%e 2, 1, 0;
%e 1, 2, 1, 0;
%e 1, 1, 2, 1, 0;
%e 1, 1, 1, 1, 1, 1;
%e 1, 1, 1, 1, 1, 1, 1;
%e 0, 2, 1, 1, 1, 1, 1, 1;
%e 0, 2, 2, 1, 0, 1, 1, 1, 1;
%e 0, 2, 2, 0, 2, 1, 0, 1, 1, 1;
%e 0, 2, 0, 2, 2, 0, 2, 1, 0, 1, 1;
%t r = Pi;
%t f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0]
%t g[n_, k_] := Sum[f[n, k, i], {i, 1, n}]
%t TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
%t Flatten[%] (* A194305 *)
%Y Cf. A194285.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Aug 21 2011