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A194816 Number of integers k in [1,n] such that {n*r+k*r} > {n*r-k*r}, where { } = fractional part and r=sqrt(2).

%I A194816 #5 Mar 30 2012 18:57:44
%S A194816 1,1,1,2,3,4,4,4,4,5,6,6,6,6,6,7,8,9,9,9,10,11,12,12,12,12,13,14,15,
%T A194816 16,16,16,17,18,19,19,19,19,20,21,21,21,21,21,22,23,24,24,24,24,25,26,
%U A194816 26,26,26,27,28,29,30,30,30,31,32,33,33,33,33,34,35,35,35,35,35
%N A194816 Number of integers k in [1,n] such that {n*r+k*r} > {n*r-k*r}, where { } = fractional part and r=sqrt(2).
%t A194816 r = Sqrt[2]; p[x_] := FractionalPart[x];
%t A194816 u[n_, k_] := If[p[n*r + k*r] <= p[n*r - k*r], 1, 0]
%t A194816 v[n_, k_] := If[p[n*r + k*r] > p[n*r - k*r], 1, 0]
%t A194816 s[n_] := Sum[u[n, k], {k, 1, n}]
%t A194816 t[n_] := Sum[v[n, k], {k, 1, n}]
%t A194816 Table[s[n], {n, 1, 100}]   (* A194815 *)
%t A194816 Table[t[n], {n, 1, 100}]   (* A194816 *)
%Y A194816 Cf. A194815, A194813.
%K A194816 nonn
%O A194816 1,4
%A A194816 _Clark Kimberling_, Sep 03 2011