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 A194333 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-tau, where tau=(1+sqrt(5))/2, the golden ratio. 2

%I #6 Mar 30 2012 18:57:43

%S 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,2,1,1,1,1,1,1,1,1,1,1,

%T 1,1,1,1,1,2,1,0,2,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,0,1,1,1,1,1,1,

%U 1,1,1,1,1,1,1,2,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,2,0,2,1,1,1,1

%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-tau, where tau=(1+sqrt(5))/2, the golden ratio.

%C See A194285.

%e First eleven rows:

%e 1

%e 1..1

%e 1..1..1

%e 1..1..1..1

%e 1..1..1..1..1

%e 1..1..1..1..1..1

%e 0..1..2..1..1..1..1

%e 1..1..1..1..1..1..1..1

%e 1..1..1..2..1..0..2..0..1

%e 1..1..1..1..1..1..1..1..1..1

%e 1..1..1..1..2..1..0..1..1..1..1

%t r = 2-GolenRatio;

%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[%] (* A194333 *)

%Y Cf. A194333.

%K nonn,tabl

%O 1,24

%A _Clark Kimberling_, Aug 22 2011

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Last modified May 21 15:47 EDT 2024. Contains 372738 sequences. (Running on oeis4.)