A194302 - OEIS

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

%S 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,3,2,2,2,2,2,3,1,3,1,2,2,2,2,2,2,2,

%T 2,2,2,2,3,2,2,2,2,2,1,2,2,2,2,3,2,1,3,2,1,2,2,3,2,1,3,1,3,1,2,2,2,1,

%U 4,1,2,3,1,3,2,2,1,2,2,2,2,3,1,2,2,2,2,2,2,2,2,2,2,2,2,1,3,3,1

%N Triangular array:  g(n,k)=number of fractional parts (i*sqrt(5)) in interval [(k-1)/n, k/n], for 1<=i<=2n, 1<=k<=n.

%C See A194285.

%e First eight rows:

%e 2

%e 2..2

%e 2..2..2

%e 2..2..2..2

%e 2..2..2..2..2

%e 1..2..3..2..2..2

%e 2..2..3..1..3..1..2

%e 2..2..2..2..2..2..2..2

%t r = 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, 2n}]

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

%t Flatten[%]    (* A194302 *)

%Y Cf. A194285.

%K nonn,tabl

%O 1,1

%A _Clark Kimberling_, Aug 21 2011