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%I #5 Mar 30 2012 18:57:43
%S 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,0,2,1,
%T 1,1,1,1,1,1,1,1,2,0,1,0,2,1,1,0,2,1,1,1,1,0,2,1,1,1,1,1,1,1,1,1,1,1,
%U 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,0,1,1,1,1,2,1,1,0,1,1
%N Triangular array: g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=n, 1<=k<=n, r=2-sqrt(2).
%C See A194285.
%e First twelve rows:
%e 1
%e 1..1
%e 1..1..1
%e 1..1..1..1
%e 1..1..1..1..1
%e 0..1..1..2..1..1
%e 1..1..1..1..1..1..1
%e 1..1..1..0..2..1..1..1
%e 1..1..1..1..1..1..2..0..1
%e 0..2..1..1..0..2..1..1..1..1
%e 0..2..1..1..1..1..1..1..1..1..1
%e 1..1..1..1..1..1..1..1..1..1..1..1
%t r = 2-Sqrt[2];
%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[%] (* A194325 *)
%Y Cf. A194285.
%K nonn,tabl
%O 1,19
%A _Clark Kimberling_, Aug 22 2011
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