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A194307 Triangular array: g(n,k) = number of fractional parts (i*Pi) in interval [(k-1)/n, k/n], for 1 <= i <= n^2, 1 <= k <= n.

%I A194307 #8 Apr 10 2021 08:04:30
%S A194307 1,3,1,4,2,3,3,5,4,4,4,5,7,3,6,6,5,5,5,8,7,7,7,7,7,7,7,7,8,7,7,7,8,9,
%T A194307 9,9,8,9,8,11,10,8,7,9,11,10,10,10,11,9,9,12,9,9,11,10,12,10,12,11,10,
%U A194307 11,12,10,11,12,9,14,11,13,14,10,13,10,13,12,11,14,8,17,11,14
%N A194307 Triangular array: g(n,k) = number of fractional parts (i*Pi) in interval [(k-1)/n, k/n], for 1 <= i <= n^2, 1 <= k <= n.
%C A194307 See A194285.
%e A194307 First eight rows:
%e A194307   1;
%e A194307   3, 1;
%e A194307   4, 2, 3;
%e A194307   3, 5, 4, 4;
%e A194307   4, 5, 7, 3, 6;
%e A194307   6, 5, 5, 5, 8, 7;
%e A194307   7, 7, 7, 7, 7, 7, 7;
%e A194307   8, 7, 7, 7, 8, 9, 9, 9;
%t A194307 r = Pi;
%t A194307 f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0]
%t A194307 g[n_, k_] := Sum[f[n, k, i], {i, 1, n^2}]
%t A194307 TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
%t A194307 Flatten[%]    (* A194307 *)
%Y A194307 Cf. A194285.
%K A194307 nonn,tabl
%O A194307 1,2
%A A194307 _Clark Kimberling_, Aug 21 2011