A194671 Number of k in [1,n] for which <n*r>+<k*r> > 1, where < > = fractional part and r = sqrt(5); row sums of A164670.

0, 0, 2, 4, 1, 2, 5, 8, 2, 4, 7, 11, 1, 4, 8, 13, 0, 4, 8, 14, 20, 4, 9, 16, 23, 4, 10, 17, 25, 2, 9, 17, 26, 0, 8, 16, 26, 36, 7, 16, 27, 38, 6, 16, 28, 40, 4, 15, 27, 40, 1, 13, 26, 40, 54, 12, 25, 40, 55, 10, 24, 40, 56, 7, 22, 38, 55, 3, 19, 36, 54, 72, 17, 34, 53, 72

Offset

1,3

Links

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

Mathematica

r = Sqrt[5]; 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}]  (* A194669 *)
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}]]
  (* A194670 *)
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}]  (* A194671 *)

Crossrefs

Cf. A194670.

Sequence in context: A035492 A101229 A057176 * A331696 A364837 A333651

Adjacent sequences: A194668 A194669 A194670 * A194672 A194673 A194674

Keyword

nonn

Author

Clark Kimberling, Sep 01 2011

Status

approved