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Number of k such that {-k*e} > {-n*e}, where { } = fractional part.
3

%I #5 Mar 30 2012 18:57:44

%S 0,0,0,3,2,1,0,6,4,2,10,7,4,1,12,8,4,17,12,7,2,18,12,6,24,17,10,3,24,

%T 16,8,31,22,13,4,30,20,10,0,29,18,7,38,26,14,2,36,23,10,46,32,18,4,43,

%U 28,13,54,38,22,6,50,33,16,62,44,26,8,57,38,19,70,50,30,10,64

%N Number of k such that {-k*e} > {-n*e}, where { } = fractional part.

%t r = -E; p[x_] := FractionalPart[x];

%t u[n_, k_] := If[p[k*r] <= p[n*r], 1, 0]

%t v[n_, k_] := If[p[k*r] > p[n*r], 1, 0]

%t s[n_] := Sum[u[n, k], {k, 1, n}]

%t t[n_] := Sum[v[n, k], {k, 1, n}]

%t Table[s[n], {n, 1, 100}] (* A194752 *)

%t Table[t[n], {n, 1, 100}] (* A194753 *)

%Y Cf. A194752.

%K nonn

%O 1,4

%A _Clark Kimberling_, Sep 02 2011