A194668 Number of k in [1,n] for which <n*r>+<k*r> > 1, where < > = fractional part and r = sqrt(3); row sums of A164667.

1, 1, 0, 4, 4, 3, 1, 7, 6, 3, 0, 9, 7, 3, 15, 12, 8, 3, 18, 14, 9, 3, 20, 15, 8, 1, 21, 14, 6, 29, 22, 14, 5, 31, 23, 13, 3, 31, 22, 11, 0, 31, 20, 8, 42, 31, 19, 6, 43, 31, 17, 3, 42, 29, 14, 56, 42, 27, 11, 56, 41, 25, 8, 55, 39, 21, 3, 53, 36, 17, 70, 52, 33, 13, 69, 50

Offset

1,4

Links

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

Mathematica

r = Sqrt[3]; z = 13;
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}]]
TableForm[Table[w[n, k], {n, 1, z}, {k, 1, n}]]
s[n_] := Sum[w[n, k], {k, 1, n}]  (* A194666 *)
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}]]
   (* A194667 *)
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}]   (* A194668 *)

Crossrefs

Cf. A194667.

Sequence in context: A016497 A259259 A369882 * A138160 A364128 A120886

Adjacent sequences: A194665 A194666 A194667 * A194669 A194670 A194671

Keyword

nonn

Author

Clark Kimberling, Sep 01 2011

Status

approved