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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=(1+sqrt(3))/2.
2

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

%S 2,3,1,2,3,3,4,5,3,4,6,7,6,7,6,11,11,12,9,11,10,19,17,19,19,17,20,17,

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

%U 103,102,101,103,103,102,186,187,185,186,187,187,185,186,187,187

%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=(1+sqrt(3))/2.

%C See A194285.

%e First six rows:

%e 2

%e 3..1

%e 2..3..3

%e 4..5..3..4

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

%e 11..11..12..9...11..10

%t r = (1+Sqrt[3])/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, 2^n}]

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

%t Flatten[%] (* A194300 *)

%Y Cf. A194285.

%K nonn,tabl

%O 1,1

%A _Clark Kimberling_, Aug 21 2011