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A194325 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). 2

%I

%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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Last modified September 24 14:46 EDT 2021. Contains 347643 sequences. (Running on oeis4.)