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A194336 Triangular array:  g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=2^n, 1<=k<=n, r=2-tau, where tau=(1+sqrt(5))/2, the golden ratio. 2

%I

%S 2,2,2,3,2,3,4,4,4,4,6,7,7,6,6,11,10,12,10,11,10,18,17,19,19,17,19,19,

%T 32,31,32,33,31,32,33,32,56,58,56,58,57,56,57,57,57,102,103,103,102,

%U 103,102,102,103,102,102,185,187,186,187,187,186,185,185,187,186

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

%C See A194285.

%e First eight rows:

%e 2

%e 2...2

%e 3...2...3

%e 4...4...4...4

%e 6...7...7...6...6

%e 11..10..12..10..11..10

%e 18..17..19..19..17..19..19

%e 32..31..32..33..31..32..33..32

%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, 2^n}]

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

%t Flatten[%] (* A194336 *)

%Y Cf. A194285.

%K nonn,tabl

%O 1,1

%A _Clark Kimberling_, Aug 22 2011

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Last modified July 22 15:12 EDT 2019. Contains 325224 sequences. (Running on oeis4.)