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A194744 Number of k such that {-k*sqrt(5)} < {-n*sqrt(5)}, where { } = fractional part.

%I A194744 #5 Mar 30 2012 18:57:44
%S A194744 1,1,1,1,5,4,3,2,9,7,5,3,13,10,7,4,17,13,9,5,1,18,13,8,3,23,17,11,5,
%T A194744 28,21,14,7,33,25,17,9,1,31,22,13,4,37,27,17,7,43,32,21,10,49,37,25,
%U A194744 13,1,44,31,18,5,51,37,23,9,58,43,28,13,65,49,33,17,1,57,40,23,6
%N A194744 Number of k such that {-k*sqrt(5)} < {-n*sqrt(5)}, where { } = fractional part.
%t A194744 r = -Sqrt[5]; p[x_] := FractionalPart[x];
%t A194744 u[n_, k_] := If[p[k*r] <= p[n*r], 1, 0]
%t A194744 v[n_, k_] := If[p[k*r] > p[n*r], 1, 0]
%t A194744 s[n_] := Sum[u[n, k], {k, 1, n}]
%t A194744 t[n_] := Sum[v[n, k], {k, 1, n}]
%t A194744 Table[s[n], {n, 1, 100}]   (* A194744 *)
%t A194744 Table[t[n], {n, 1, 100}]   (* A194745 *)
%Y A194744 Cf. A194745, A194738.
%K A194744 nonn
%O A194744 1,5
%A A194744 _Clark Kimberling_, Sep 02 2011