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A194814 Number of integers k in [1,n] such that {n*r+k*r} > {n*r-k*r}, where { } = fractional part and r=(1+sqrt(5))/2 (the golden ratio).

%I A194814 #6 Mar 30 2012 18:57:44
%S A194814 1,2,2,2,3,4,4,4,4,5,6,6,7,8,9,9,9,10,11,11,11,11,12,12,12,13,14,15,
%T A194814 15,15,16,17,17,18,19,20,20,20,21,22,22,22,22,23,23,23,24,25,26,26,26,
%U A194814 27,28,28,28,28,29,29,29,30,31,31,31,31,32,33,33,34,35,36,36,36
%N A194814 Number of integers k in [1,n] such that {n*r+k*r} > {n*r-k*r}, where { } = fractional part and r=(1+sqrt(5))/2 (the golden ratio).
%C A194814 A194813+A194814=A000027 for n>0.
%e A194814 {4r+1r}=0.09...; {4r-1r}=0.85...;
%e A194814 {4r+2r}=0.70...; {4r-2r}=0.23...;
%e A194814 {4r+3r}=0.32...; {4r-3r}=0.61...;
%e A194814 {4r+4r}=0.94...; {4r-4r}=0.00...;
%e A194814 so that a(4)=2.
%t A194814 r = GoldenRatio; p[x_] := FractionalPart[x];
%t A194814 u[n_, k_] := If[p[n*r + k*r] <= p[n*r - k*r], 1, 0]
%t A194814 v[n_, k_] := If[p[n*r + k*r] > p[n*r - k*r], 1, 0]
%t A194814 s[n_] := Sum[u[n, k], {k, 1, n}]
%t A194814 t[n_] := Sum[v[n, k], {k, 1, n}]
%t A194814 Table[s[n], {n, 1, 100}]   (* A194813 *)
%t A194814 Table[t[n], {n, 1, 100}]   (* A194814 *)
%Y A194814 Cf. A194813, A194738.
%K A194814 nonn
%O A194814 1,2
%A A194814 _Clark Kimberling_, Sep 03 2011