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

%I #5 Mar 30 2012 18:57:42

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

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

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

%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<=2^n, r=(1+sqrt(5))/2, the golden ratio.

%C See A194285.

%e First seven rows:

%e 2

%e 2...2

%e 3...2...3

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

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

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

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

%t r = 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[%] (* A194296 *)

%Y Cf. A194285.

%K nonn,tabl

%O 1,1

%A _Clark Kimberling_, Aug 21 2011