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A194815 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 A194815 #10 Jun 25 2022 10:01:42
%S A194815 0,1,2,2,2,2,3,4,5,5,5,6,7,8,9,9,9,9,10,11,11,11,11,12,13,14,14,14,14,
%T A194815 14,15,16,16,16,16,17,18,19,19,19,20,21,22,23,23,23,23,24,25,26,26,26,
%U A194815 27,28,29,29,29,29,29,30,31,31,31,31,32,33,34,34,34,35,36,37
%N A194815 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 A194815 r = Sqrt[2]; p[x_] := FractionalPart[x];
%t A194815 u[n_, k_] := If[p[n*r + k*r] <= p[n*r - k*r], 1, 0]
%t A194815 v[n_, k_] := If[p[n*r + k*r] > p[n*r - k*r], 1, 0]
%t A194815 s[n_] := Sum[u[n, k], {k, 1, n}]
%t A194815 t[n_] := Sum[v[n, k], {k, 1, n}]
%t A194815 Table[s[n], {n, 1, 100}]   (* A194815 *)
%t A194815 Table[t[n], {n, 1, 100}]   (* A194816 *)
%Y A194815 Cf. A002193, A194816, A194813.
%Y A194815 Partial sums of A327177.
%K A194815 nonn
%O A194815 1,3
%A A194815 _Clark Kimberling_, Sep 03 2011