A194678 Number of k in [1,n] for which <n*e>+<k*e> > 1, where < > = fractional part; row sums of A164677.

1, 1, 0, 4, 4, 2, 0, 6, 4, 1, 10, 8, 4, 0, 11, 7, 2, 16, 12, 7, 1, 17, 12, 5, 24, 18, 11, 3, 24, 17, 8, 32, 24, 15, 5, 31, 22, 11, 0, 29, 18, 6, 38, 27, 14, 1, 35, 22, 8, 45, 32, 17, 2, 41, 27, 11, 53, 38, 22, 5, 49, 33, 15, 62, 45, 27, 8, 57, 39, 19, 71, 52, 32, 11, 66, 46

Offset

1,4

Links

Table of n, a(n) for n=1..76.

Mathematica

r = E; z = 15;
p[x_] := FractionalPart[x]; f[x_] := Floor[x];
w[n_, k_] := p[r^n] + p[r^k] - p[r^n + r^k]
Flatten[Table[w[n, k], {n, 1, z}, {k, 1, n}]]
(* A194675 *)
TableForm[Table[w[n, k], {n, 1, z}, {k, 1, n}]]
s[n_] := Sum[w[n, k], {k, 1, n}]  (* A194676 *)
Table[s[n], {n, 1, 100}]
h[n_, k_] := f[p[n*r] + p[k*r]]
Flatten[Table[h[n, k], {n, 1, z}, {k, 1, n}]]
 (* A194677 *)
TableForm[Table[h[n, k], {n, 1, z}, {k, 1, n}]]
t[n_] := Sum[h[n, k], {k, 1, n}]
Table[t[n], {n, 1, 100}]  (* A194678 *)

Crossrefs

Cf. A194677.

Sequence in context: A173210 A328922 A058888 * A153015 A173635 A196766

Adjacent sequences: A194675 A194676 A194677 * A194679 A194680 A194681

Keyword

nonn

Author

Clark Kimberling, Sep 01 2011

Status

approved