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A194819 Number of integers k in [1,n] such that {n*e+k*e} < {n*e-k*e}, where { } = fractional part.

%I A194819 #10 Jun 25 2022 10:01:33
%S A194819 0,1,1,2,3,3,3,3,4,4,5,6,6,6,6,7,7,8,9,10,10,10,11,11,12,13,14,14,14,
%T A194819 15,15,16,17,18,18,18,19,19,19,19,20,20,21,22,22,22,22,23,23,24,25,25,
%U A194819 25,25,26,26,27,28,29,29,29,30,30,31,32,33,33,33,34,34,35,36,37
%N A194819 Number of integers k in [1,n] such that {n*e+k*e} < {n*e-k*e}, where { } = fractional part.
%t A194819 r = E; p[x_] := FractionalPart[x];
%t A194819 u[n_, k_] := If[p[n*r + k*r] <= p[n*r - k*r], 1, 0]
%t A194819 v[n_, k_] := If[p[n*r + k*r] > p[n*r - k*r], 1, 0]
%t A194819 s[n_] := Sum[u[n, k], {k, 1, n}]
%t A194819 t[n_] := Sum[v[n, k], {k, 1, n}]
%t A194819 Table[s[n], {n, 1, 100}]   (* A194819 *)
%t A194819 Table[t[n], {n, 1, 100}]   (* A194820 *)
%Y A194819 Cf. A001113, A194820.
%Y A194819 Partial sums of A327183.
%K A194819 nonn
%O A194819 1,4
%A A194819 _Clark Kimberling_, Sep 03 2011