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A194817 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 A194817 #10 Jun 25 2022 10:01:38
%S A194817 0,1,1,2,3,4,4,4,5,5,5,5,6,6,7,8,9,9,10,11,12,12,12,13,13,13,13,14,14,
%T A194817 15,16,17,17,18,19,19,19,19,20,20,20,20,21,21,22,23,24,24,25,26,26,26,
%U A194817 26,27,27,28,29,30,30,31,32,33,33,33,34,34,34,34,35,35,36,37
%N A194817 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 A194817 r = Sqrt[3]; p[x_] := FractionalPart[x];
%t A194817 u[n_, k_] := If[p[n*r + k*r] <= p[n*r - k*r], 1, 0]
%t A194817 v[n_, k_] := If[p[n*r + k*r] > p[n*r - k*r], 1, 0]
%t A194817 s[n_] := Sum[u[n, k], {k, 1, n}]
%t A194817 t[n_] := Sum[v[n, k], {k, 1, n}]
%t A194817 Table[s[n], {n, 1, 100}]   (* A194817 *)
%t A194817 Table[t[n], {n, 1, 100}]   (* A194818 *)
%Y A194817 Cf. A002194, A194818, A194813.
%Y A194817 Partial sums of A327180.
%K A194817 nonn
%O A194817 1,4
%A A194817 _Clark Kimberling_, Sep 03 2011