A194815 Number of integers k in [1,n] such that {n*r+k*r} < {n*r-k*r}, where { } = fractional part and r=sqrt(2).

0, 1, 2, 2, 2, 2, 3, 4, 5, 5, 5, 6, 7, 8, 9, 9, 9, 9, 10, 11, 11, 11, 11, 12, 13, 14, 14, 14, 14, 14, 15, 16, 16, 16, 16, 17, 18, 19, 19, 19, 20, 21, 22, 23, 23, 23, 23, 24, 25, 26, 26, 26, 27, 28, 29, 29, 29, 29, 29, 30, 31, 31, 31, 31, 32, 33, 34, 34, 34, 35, 36, 37

Offset

1,3

Links

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

Mathematica

r = Sqrt[2]; 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}]   (* A194815 *)
Table[t[n], {n, 1, 100}]   (* A194816 *)

Crossrefs

Cf. A002193, A194816, A194813.

Partial sums of A327177.

Sequence in context: A202276 A029115 A029101 * A029080 A147652 A058360

Adjacent sequences: A194812 A194813 A194814 * A194816 A194817 A194818

Keyword

nonn

Author

Clark Kimberling, Sep 03 2011

Status

approved