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A194764 Number of k such that {-k*2^(1/3)} < {-n*2^(1/3)}, where { } = fractional part.

%I A194764 #5 Mar 30 2012 18:57:44
%S A194764 1,1,1,4,3,2,1,7,5,3,1,10,7,4,1,13,9,5,1,16,11,6,1,19,13,7,27,20,13,6,
%T A194764 29,21,13,5,31,22,13,4,33,23,13,3,35,24,13,2,37,25,13,1,39,26,13,53,
%U A194764 39,25,11,54,39,24,9,55,39,23,7,56,39,22,5,57,39,21,3,58,39,20
%N A194764 Number of k such that {-k*2^(1/3)} < {-n*2^(1/3)}, where { } = fractional part.
%t A194764 r = -2^(1/3); p[x_] := FractionalPart[x];
%t A194764 u[n_, k_] := If[p[k*r] <= p[n*r], 1, 0]
%t A194764 v[n_, k_] := If[p[k*r] > p[n*r], 1, 0]
%t A194764 s[n_] := Sum[u[n, k], {k, 1, n}]
%t A194764 t[n_] := Sum[v[n, k], {k, 1, n}]
%t A194764 Table[s[n], {n, 1, 100}]  (* A194764 *)
%t A194764 Table[t[n], {n, 1, 100}]  (* A194765 *)
%Y A194764 Cf. A194765, A194738.
%K A194764 nonn
%O A194764 1,4
%A A194764 _Clark Kimberling_, Sep 02 2011