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A194739 Number of k such that {k*sqrt(3)} > {n*sqrt(3)}, where { } = fractional part.

%I A194739 #6 Mar 30 2012 18:57:44
%S A194739 0,1,2,0,2,4,6,1,4,7,10,2,6,10,0,5,10,15,2,8,14,20,4,11,18,25,6,14,22,
%T A194739 1,10,19,28,4,14,24,34,7,18,29,40,10,22,34,2,15,28,41,6,20,34,48,10,
%U A194739 25,40,0,16,32,48,5,22,39,56,10,28,46,64,15,34,53,2,22,42,62,8
%N A194739 Number of k such that {k*sqrt(3)} > {n*sqrt(3)}, where { } = fractional part.
%t A194739 r = Sqrt[3]; p[x_] := FractionalPart[x];
%t A194739 u[n_, k_] := If[p[k*r] <= p[n*r], 1, 0]
%t A194739 v[n_, k_] := If[p[k*r] > p[n*r], 1, 0]
%t A194739 s[n_] := Sum[u[n, k], {k, 1, n}]
%t A194739 t[n_] := Sum[v[n, k], {k, 1, n}]
%t A194739 Table[s[n], {n, 1, 100}]   (* A194738 *)
%t A194739 Table[t[n], {n, 1, 100}]   (* A194739 *)
%Y A194739 Cf. A194738.
%K A194739 nonn
%O A194739 1,3
%A A194739 _Clark Kimberling_, Sep 02 2011