A194682 Number of k in [1,n] for which <n*r>+<k*r> > 1, where < > = fractional part, and r=3-sqrt(2); row sums of A164681.

1, 0, 2, 1, 5, 4, 1, 6, 2, 9, 5, 0, 8, 2, 11, 5, 16, 10, 2, 14, 6, 20, 11, 1, 16, 5, 22, 11, 29, 18, 5, 24, 11, 32, 19, 4, 26, 10, 34, 18, 1, 26, 8, 34, 16, 44, 26, 6, 35, 14, 45, 24, 2, 34, 11, 45, 22, 57, 34, 9, 45, 20, 58, 32, 5, 44, 16, 57, 29, 0, 42, 12, 55, 25, 70, 40

Offset

1,3

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

Mathematica

r = 3 - Sqrt[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}]]
  (* A194679 *)
TableForm[Table[w[n, k], {n, 1, z}, {k, 1, n}]]
s[n_] := Sum[w[n, k], {k, 1, n}]  (* A194680 *)
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}]]
  (* A194681 *)
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}]   (* A194682 *)

Prog

(PARI) for(n=1, 50, print1(sum(k=1, n, floor(frac(n*(3-sqrt(2))) + frac(k*(3-sqrt(2))))), ", ")) \\ G. C. Greubel, Feb 08 2018

Crossrefs

Cf. A194681.

Sequence in context: A141506 A345454 A271684 * A274105 A366156 A056242

Adjacent sequences: A194679 A194680 A194681 * A194683 A194684 A194685

Keyword

nonn

Author

Clark Kimberling, Sep 01 2011

Status

approved