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A194748 Number of k such that {-k*sqrt(6)} < {-n*sqrt(6)}, where { } = fractional part.

%I A194748 #5 Mar 30 2012 18:57:44
%S A194748 1,1,3,2,5,3,7,4,9,5,1,8,3,11,5,14,7,17,9,1,13,4,17,7,21,10,25,13,29,
%T A194748 16,3,21,7,26,11,31,15,36,19,2,25,7,31,12,37,17,43,22,49,27,5,34,11,
%U A194748 41,17,48,23,55,29,3,37,10,45,17,53,24,61,31,69,38,7,47,15,56,23
%N A194748 Number of k such that {-k*sqrt(6)} < {-n*sqrt(6)}, where { } = fractional part.
%t A194748 r = -Sqrt[6]; p[x_] := FractionalPart[x];
%t A194748 u[n_, k_] := If[p[k*r] <= p[n*r], 1, 0]
%t A194748 v[n_, k_] := If[p[k*r] > p[n*r], 1, 0]
%t A194748 s[n_] := Sum[u[n, k], {k, 1, n}]
%t A194748 t[n_] := Sum[v[n, k], {k, 1, n}]
%t A194748 Table[s[n], {n, 1, 100}]   (* A194748 *)
%t A194748 Table[t[n], {n, 1, 100}]   (* A194749 *)
%Y A194748 Cf. A194749, A194738.
%K A194748 nonn
%O A194748 1,3
%A A194748 _Clark Kimberling_, Sep 02 2011