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A194308 Triangular array: g(n,k) = number of fractional parts (i*Pi) in interval [(k-1)/n, k/n], for 1 <= i <= 2^n, 1 <= k <= n.

%I A194308 #8 Apr 10 2021 08:04:37
%S A194308 2,3,1,3,2,3,3,5,4,4,5,7,8,4,8,10,9,10,12,12,11,19,18,18,18,18,18,19,
%T A194308 31,31,32,32,32,32,32,34,53,58,55,61,55,57,53,60,60,99,100,100,108,
%U A194308 100,100,108,100,100,109,180,182,180,200,182,180,182,200,180,182
%N A194308 Triangular array: g(n,k) = number of fractional parts (i*Pi) in interval [(k-1)/n, k/n], for 1 <= i <= 2^n, 1 <= k <= n.
%C A194308 See A194285.
%e A194308 First six rows:
%e A194308    2;
%e A194308    3,  1;
%e A194308    3,  2,  3;
%e A194308    3,  5,  4,  4;
%e A194308    5,  7,  8,  4,  8;
%e A194308   10,  9, 10, 12, 12, 11;
%t A194308 r = Pi;
%t A194308 f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0]
%t A194308 g[n_, k_] := Sum[f[n, k, i], {i, 1, 2^n}]
%t A194308 TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
%t A194308 Flatten[%]    (* A194308 *)
%Y A194308 Cf. A194285.
%K A194308 nonn,tabl
%O A194308 1,1
%A A194308 _Clark Kimberling_, Aug 21 2011