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A194321 Triangular array: g(n,k)=number of fractional parts (i*sqrt(1/2)) in interval [(k-1)/n, k/n], for 1<=i<=n, 1<=k<=n.

%I A194321 #11 Jun 04 2022 22:04:11
%S A194321 1,1,1,1,1,1,1,1,1,1,1,0,2,1,1,1,1,1,1,2,0,1,1,1,1,1,1,1,1,1,0,1,1,2,
%T A194321 1,1,0,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,2,1,0,2,1,1,1,1,1,
%U A194321 1,0,2,1,1,1,1,2,0,1,1,1,1,1,1,1,2,0,1,1,2,0,1,1,1,1,1,0,2,1,1,0
%N A194321 Triangular array:  g(n,k)=number of fractional parts (i*sqrt(1/2)) in interval [(k-1)/n, k/n], for 1<=i<=n, 1<=k<=n.
%C A194321 See A194285.
%e A194321 First eleven rows:
%e A194321 1
%e A194321 1..1
%e A194321 1..1..1
%e A194321 1..1..1..1
%e A194321 1..0..2..1..1
%e A194321 1..1..1..1..2..0
%e A194321 1..1..1..1..1..1..1
%e A194321 1..1..0..1..1..2..1..1
%e A194321 0..1..1..2..1..1..1..1..1
%e A194321 1..1..1..1..1..1..1..1..1..1
%e A194321 1..1..1..0..2..1..0..2..1..1..1
%t A194321 r = Sqrt[1/2];
%t A194321 f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0]
%t A194321 g[n_, k_] := Sum[f[n, k, i], {i, 1, n}]
%t A194321 TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
%t A194321 Flatten[%]    (* A194321 *)
%Y A194321 Cf. A194285.
%K A194321 nonn,tabl
%O A194321 1,13
%A A194321 _Clark Kimberling_, Aug 22 2011