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A194820 Number of integers k in [1,n] such that {n*e+k*e} > {n*e-k*e}, where { } = fractional part.

%I A194820 #5 Mar 30 2012 18:57:44
%S A194820 1,1,2,2,2,3,4,5,5,6,6,6,7,8,9,9,10,10,10,10,11,12,12,13,13,13,13,14,
%T A194820 15,15,16,16,16,16,17,18,18,19,20,21,21,22,22,22,23,24,25,25,26,26,26,
%U A194820 27,28,29,29,30,30,30,30,31,32,32,33,33,33,33,34,35,35,36,36,36
%N A194820 Number of integers k in [1,n] such that {n*e+k*e} > {n*e-k*e}, where { } = fractional part.
%t A194820 r = E; p[x_] := FractionalPart[x];
%t A194820 u[n_, k_] := If[p[n*r + k*r] <= p[n*r - k*r], 1, 0]
%t A194820 v[n_, k_] := If[p[n*r + k*r] > p[n*r - k*r], 1, 0]
%t A194820 s[n_] := Sum[u[n, k], {k, 1, n}]
%t A194820 t[n_] := Sum[v[n, k], {k, 1, n}]
%t A194820 Table[s[n], {n, 1, 100}]   (* A194819 *)
%t A194820 Table[t[n], {n, 1, 100}]   (* A194820 *)
%Y A194820 Cf. A194819, A194813.
%K A194820 nonn
%O A194820 1,3
%A A194820 _Clark Kimberling_, Sep 03 2011