A194815 -id:A194815 - cp's OEIS frontend

A194816 Number of integers k in [1,n] such that {nr+kr} > {nr-kr}, where { } = fractional part and r=sqrt(2).

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Offset: 1

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Clark Kimberling, Sep 03 2011

nonn

Cf. A194815, A194813.

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 *)

cp's OEIS Frontend

A194816 Number of integers k in [1,n] such that {nr+kr} > {nr-kr}, where { } = fractional part and r=sqrt(2).

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cp's OEIS Frontend

A194816 Number of integers k in [1,n] such that {n*r+k*r} > {n*r-k*r}, where { } = fractional part and r=sqrt(2).

Views

Author

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Crossrefs

Programs

Mathematica

A194816 Number of integers k in [1,n] such that {nr+kr} > {nr-kr}, where { } = fractional part and r=sqrt(2).