|
%I #5 Mar 30 2012 18:57:42
%S 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,0,1,1,1,1,1,1,
%T 1,1,1,0,2,0,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,2,1,1,1,1,0,1,
%U 2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
%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<=n, r=(1+sqrt(5))/2, the golden ratio.
%C See A194285. Which rows are constant?
%e First ten rows:
%e 1
%e 1..1
%e 1..1..1
%e 1..1..1..1
%e 1..1..1..1..1
%e 1..1..1..1..1..1
%e 1..1..1..1..2..1..0
%e 1..1..1..1..1..1..1..1
%e 1..0..2..0..1..2..1..1..1
%e 1..1..1..1..1..1..1..1..1..1
%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, n}]
%t TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
%t Flatten[%] (* A194293 *)
%Y Cf. A194293.
%K nonn,tabl
%O 1,26
%A _Clark Kimberling_, Aug 21 2011
|
