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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). 2

%I

%S 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 15,15,16,17,17,18,19,20,20,20,21,22,22,22,22,23,23,23,24,25,26,26,26,

%U 27,28,28,28,28,29,29,29,30,31,31,31,31,32,33,33,34,35,36,36,36

%N 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 A194813+A194814=A000027 for n>0.

%e {4r+1r}=0.09...; {4r-1r}=0.85...;

%e {4r+2r}=0.70...; {4r-2r}=0.23...;

%e {4r+3r}=0.32...; {4r-3r}=0.61...;

%e {4r+4r}=0.94...; {4r-4r}=0.00...;

%e so that a(4)=2.

%t r = GoldenRatio; p[x_] := FractionalPart[x];

%t u[n_, k_] := If[p[n*r + k*r] <= p[n*r - k*r], 1, 0]

%t v[n_, k_] := If[p[n*r + k*r] > p[n*r - k*r], 1, 0]

%t s[n_] := Sum[u[n, k], {k, 1, n}]

%t t[n_] := Sum[v[n, k], {k, 1, n}]

%t Table[s[n], {n, 1, 100}] (* A194813 *)

%t Table[t[n], {n, 1, 100}] (* A194814 *)

%Y Cf. A194813, A194738.

%K nonn

%O 1,2

%A _Clark Kimberling_, Sep 03 2011

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Last modified October 1 11:02 EDT 2022. Contains 357147 sequences. (Running on oeis4.)