login
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=3-sqrt(5).
2

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

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

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

%U 101,105,102,102,102,103,187,184,188,185,186,187,186,187,185,188

%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=3-sqrt(5).

%C See A194285.

%e First six rows:

%e 2

%e 2...2

%e 3...3...2

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

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

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

%t r = 3-Sqrt[5];

%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[%] (* A194340 *)

%Y Cf. A194285.

%K nonn,tabl

%O 1,1

%A _Clark Kimberling_, Aug 22 2011