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A194747 Number of k such that {k*sqrt(6)} > {n*sqrt(6)}, where { } = fractional part.

%I A194747 #6 Mar 30 2012 18:57:44
%S A194747 0,0,2,1,4,2,6,3,8,4,0,7,2,10,4,13,6,16,8,0,12,3,16,6,20,9,24,12,28,
%T A194747 15,2,20,6,25,10,30,14,35,18,1,24,6,30,11,36,16,42,21,48,26,4,33,10,
%U A194747 40,16,47,22,54,28,2,36,9,44,16,52,23,60,30,68,37,6,46,14,55,22,64
%N A194747 Number of k such that {k*sqrt(6)} > {n*sqrt(6)}, where { } = fractional part.
%t A194747 r = Sqrt[6]; p[x_] := FractionalPart[x];
%t A194747 u[n_, k_] := If[p[k*r] <= p[n*r], 1, 0]
%t A194747 v[n_, k_] := If[p[k*r] > p[n*r], 1, 0]
%t A194747 s[n_] := Sum[u[n, k], {k, 1, n}]
%t A194747 t[n_] := Sum[v[n, k], {k, 1, n}]
%t A194747 Table[s[n], {n, 1, 100}]   (* A194746 *)
%t A194747 Table[t[n], {n, 1, 100}]   (* A194747 *)
%Y A194747 Cf. A194746, A194738.
%K A194747 nonn
%O A194747 1,3
%A A194747 _Clark Kimberling_, Sep 02 2011