A194820 Number of integers k in [1,n] such that {n*e+k*e} > {n*e-k*e}, where { } = fractional part.

1, 1, 2, 2, 2, 3, 4, 5, 5, 6, 6, 6, 7, 8, 9, 9, 10, 10, 10, 10, 11, 12, 12, 13, 13, 13, 13, 14, 15, 15, 16, 16, 16, 16, 17, 18, 18, 19, 20, 21, 21, 22, 22, 22, 23, 24, 25, 25, 26, 26, 26, 27, 28, 29, 29, 30, 30, 30, 30, 31, 32, 32, 33, 33, 33, 33, 34, 35, 35, 36, 36, 36

Offset

1,3

Links

Table of n, a(n) for n=1..72.

Mathematica

r = E; p[x_] := FractionalPart[x];
u[n_, k_] := If[p[n*r + k*r] <= p[n*r - k*r], 1, 0]
v[n_, k_] := If[p[n*r + k*r] > p[n*r - k*r], 1, 0]
s[n_] := Sum[u[n, k], {k, 1, n}]
t[n_] := Sum[v[n, k], {k, 1, n}]
Table[s[n], {n, 1, 100}]   (* A194819 *)
Table[t[n], {n, 1, 100}]   (* A194820 *)

Crossrefs

Cf. A194819, A194813.

Sequence in context: A096533 A230413 A029096 * A076872 A008906 A029074

Adjacent sequences: A194817 A194818 A194819 * A194821 A194822 A194823

Keyword

nonn

Author

Clark Kimberling, Sep 03 2011

Status

approved