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A194818 Number of integers k in [1,n] such that {n*r+k*r} > {n*r-k*r}, where { } = fractional part and r=sqrt(3).

%I A194818 #5 Mar 30 2012 18:57:44
%S A194818 1,1,2,2,2,2,3,4,4,5,6,7,7,8,8,8,8,9,9,9,9,10,11,11,12,13,14,14,15,15,
%T A194818 15,15,16,16,16,17,18,19,19,20,21,22,22,23,23,23,23,24,24,24,25,26,27,
%U A194818 27,28,28,28,28,29,29,29,29,30,31,31,32,33,34,34,35,35,35,35
%N A194818 Number of integers k in [1,n] such that {n*r+k*r} > {n*r-k*r}, where { } = fractional part and r=sqrt(3).
%t A194818 r = Sqrt[3]; p[x_] := FractionalPart[x];
%t A194818 u[n_, k_] := If[p[n*r + k*r] <= p[n*r - k*r], 1, 0]
%t A194818 v[n_, k_] := If[p[n*r + k*r] > p[n*r - k*r], 1, 0]
%t A194818 s[n_] := Sum[u[n, k], {k, 1, n}]
%t A194818 t[n_] := Sum[v[n, k], {k, 1, n}]
%t A194818 Table[s[n], {n, 1, 100}]   (* A194817 *)
%t A194818 Table[t[n], {n, 1, 100}]   (* A194818 *)
%Y A194818 Cf. A194817, A194813.
%K A194818 nonn
%O A194818 1,3
%A A194818 _Clark Kimberling_, Sep 03 2011