A194686 Number of k in [1,n] for which <n*r>+<k*r> > 1, where < > = fractional part, and r=(1+sqrt(3))/2; row sums of A164685.

0, 2, 0, 1, 4, 1, 4, 8, 3, 7, 0, 4, 10, 1, 6, 13, 3, 10, 18, 6, 15, 1, 9, 19, 3, 13, 24, 7, 18, 30, 11, 24, 3, 15, 29, 6, 20, 35, 11, 26, 0, 15, 32, 4, 20, 38, 9, 27, 46, 15, 34, 1, 20, 41, 6, 26, 48, 12, 34, 57, 19, 43, 3, 26, 51, 9, 34, 60, 17, 43, 70, 25, 53, 6, 33, 62

Offset

1,2

Links

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

Mathematica

r = 1/2 + Sqrt[3]/2; 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}]]
  (* A194683 *)
TableForm[Table[w[n, k], {n, 1, z}, {k, 1, n}]]
s[n_] := Sum[w[n, k], {k, 1, n}]
Table[s[n], {n, 1, 100}]   (* A194684 *)
h[n_, k_] := f[p[n*r] + p[k*r]]
Flatten[Table[h[n, k], {n, 1, z}, {k, 1, n}]]
  (* A194685 *)
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}]    (* A194686 *)

Crossrefs

Cf. A194684.

Sequence in context: A228924 A246862 A338773 * A302996 A266213 A289522

Adjacent sequences: A194683 A194684 A194685 * A194687 A194688 A194689

Keyword

nonn

Author

Clark Kimberling, Sep 01 2011

Status

approved