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 A194334 Triangular array: g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=2n, 1<=k<=n, r=2-tau, where tau=(1+sqrt(5))/2, the golden ratio. 2

%I #5 Mar 30 2012 18:57:43

%S 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,1,1,2,3,2,2,2,2,2,2,2,2,2,2,

%T 2,2,1,3,1,3,2,1,3,2,2,1,2,3,2,2,2,2,2,2,2,2,2,2,2,3,2,1,2,2,2,2,2,2,

%U 2,2,3,2,1,2,2,3,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,3,1,3,2,2,2

%N Triangular array: g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=2n, 1<=k<=n, r=2-tau, where tau=(1+sqrt(5))/2, the golden ratio.

%C See A194285.

%e First nine rows:

%e 2

%e 2..2

%e 2..2..2

%e 2..2..2..2

%e 2..2..2..2..2

%e 2..2..2..2..3..1

%e 1..2..3..2..2..2..2

%e 2..2..2..2..2..2..2..2

%e 1..3..1..3..2..1..3..2..2

%t r = 2-GoldenRatio;

%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, 2n}]

%t TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]

%t Flatten[%] (* A194334 *)

%Y Cf. A194285.

%K nonn,tabl

%O 1,1

%A _Clark Kimberling_, Aug 22 2011

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Last modified April 17 08:35 EDT 2024. Contains 371763 sequences. (Running on oeis4.)