cp's OEIS Frontend

A194745 Number of k such that {-k*sqrt(5)} > {-n*sqrt(5)}, where { } = fractional part.

%I A194745 #6 Mar 30 2012 18:57:44
%S A194745 0,1,2,3,0,2,4,6,0,3,6,9,0,4,8,12,0,5,10,15,20,4,10,16,22,3,10,17,24,
%T A194745 2,10,18,26,1,10,19,28,37,8,18,28,38,6,17,28,39,4,16,28,40,2,15,28,41,
%U A194745 54,12,26,40,54,9,24,39,54,6,22,38,54,3,20,37,54,71,16,34,52,70
%N A194745 Number of k such that {-k*sqrt(5)} > {-n*sqrt(5)}, where { } = fractional part.
%t A194745 r = -Sqrt[5]; p[x_] := FractionalPart[x];
%t A194745 u[n_, k_] := If[p[k*r] <= p[n*r], 1, 0]
%t A194745 v[n_, k_] := If[p[k*r] > p[n*r], 1, 0]
%t A194745 s[n_] := Sum[u[n, k], {k, 1, n}]
%t A194745 t[n_] := Sum[v[n, k], {k, 1, n}]
%t A194745 Table[s[n], {n, 1, 100}]   (* A194744 *)
%t A194745 Table[t[n], {n, 1, 100}]   (* A194745 *)
%Y A194745 Cf. A194744, A194738.
%K A194745 nonn
%O A194745 1,3
%A A194745 _Clark Kimberling_, Sep 02 2011