A194665 Number of k in [1,n] for which <n*r>+<k*r> > 1, where < > = fractional part and r = sqrt(2); row sums of A164664.

0, 2, 1, 3, 0, 2, 6, 2, 7, 1, 6, 12, 5, 12, 4, 11, 1, 8, 17, 6, 15, 2, 12, 23, 9, 21, 5, 17, 0, 12, 26, 8, 22, 2, 16, 32, 11, 28, 5, 22, 40, 16, 35, 10, 29, 2, 21, 42, 14, 36, 6, 28, 51, 20, 44, 11, 35, 1, 25, 51, 16, 42, 5, 32, 60, 22, 51, 11, 40, 70, 29, 60, 18, 49, 5, 36

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Mathematica

r = Sqrt[2]; 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}]  (* A194663 *)
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}]]
   (* A194664 *)
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}]    (* A194665 *)

Crossrefs

Cf. A194664.

Sequence in context: A025643 A127478 A127472 * A004563 A329647 A364235

Adjacent sequences: A194662 A194663 A194664 * A194666 A194667 A194668

Keyword

nonn

Author

Clark Kimberling, Sep 01 2011

Status

approved