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A194743 Number of k such that {k*sqrt(5)} > {n*sqrt(5)}, where { } = fractional part.

%I A194743 #6 Mar 30 2012 18:57:44
%S A194743 0,0,0,0,4,3,2,1,8,6,4,2,12,9,6,3,16,12,8,4,0,17,12,7,2,22,16,10,4,27,
%T A194743 20,13,6,32,24,16,8,0,30,21,12,3,36,26,16,6,42,31,20,9,48,36,24,12,0,
%U A194743 43,30,17,4,50,36,22,8,57,42,27,12,64,48,32,16,0,56,39,22,5,64
%N A194743 Number of k such that {k*sqrt(5)} > {n*sqrt(5)}, where { } = fractional part.
%t A194743 r = Sqrt[5]; p[x_] := FractionalPart[x];
%t A194743 u[n_, k_] := If[p[k*r] <= p[n*r], 1, 0]
%t A194743 v[n_, k_] := If[p[k*r] > p[n*r], 1, 0]
%t A194743 s[n_] := Sum[u[n, k], {k, 1, n}]
%t A194743 t[n_] := Sum[v[n, k], {k, 1, n}]
%t A194743 Table[s[n], {n, 1, 100}]   (* A194742 *)
%t A194743 Table[t[n], {n, 1, 100}]   (* A194743 *)
%Y A194743 Cf. A194743, A194738.
%K A194743 nonn
%O A194743 1,5
%A A194743 _Clark Kimberling_, Sep 02 2011