A194662 Number of k in [1,n] for which <n*r>+<k*r> > 1, where < > = fractional part and r = (1+sqrt(5))/2 (the golden ratio); row sums of A164661.

1, 0, 3, 2, 0, 4, 2, 8, 6, 2, 9, 5, 0, 9, 3, 14, 9, 2, 14, 7, 21, 14, 5, 21, 12, 2, 19, 8, 27, 17, 5, 25, 13, 0, 22, 8, 32, 18, 3, 28, 13, 40, 25, 8, 37, 20, 2, 32, 13, 45, 27, 7, 40, 20, 55, 35, 13, 50, 28, 5, 43, 20, 60, 37, 12, 53, 28, 2, 45, 18, 63, 36, 8, 54, 26, 74, 46

Offset

1,3

Links

Table of n, a(n) for n=1..77.

Mathematica

r = GoldenRatio; z = 14;
p[x_] := FractionalPart[x]; f[x_] := Floor[x];
h[n_, k_] := f[p[n*r] + p[k*r]]
Flatten[Table[h[n, k], {n, 1, z}, {k, 1, n}]]  (* A194661 *)
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}]   (* A194662 *)

Crossrefs

Cf. A194661.

Sequence in context: A328178 A127571 A377524 * A143612 A353160 A011231

Adjacent sequences: A194659 A194660 A194661 * A194663 A194664 A194665

Keyword

nonn

Author

Clark Kimberling, Sep 01 2011

Status

approved