A194902 Triangular array (and fractal sequence): row n is the permutation of (1,2,...,n) obtained from the increasing ordering of fractional parts {r}, {2r}, ..., {nr}, where r=-sqrt(12).

1, 2, 1, 2, 1, 3, 2, 4, 1, 3, 2, 4, 1, 3, 5, 2, 4, 6, 1, 3, 5, 2, 4, 6, 1, 3, 5, 7, 2, 4, 6, 8, 1, 3, 5, 7, 2, 4, 6, 8, 1, 3, 5, 7, 9, 2, 4, 6, 8, 10, 1, 3, 5, 7, 9, 2, 4, 6, 8, 10, 1, 3, 5, 7, 9, 11, 2, 4, 6, 8, 10, 12, 1, 3, 5, 7, 9, 11, 2, 4, 6, 8, 10, 12, 1, 3, 5, 7, 9, 11, 13, 2, 4, 6

Offset

1,2

Comments

See A194832 for a general discussion.

Links

Table of n, a(n) for n=1..94.

Example

First nine rows:
1
2 1
2 1 3
2 4 1 3
2 4 6 1 3 5
2 4 6 1 3 5 7
2 4 6 8 1 3 5 7
2 4 6 8 1 3 5 7 9

Mathematica

r = -Sqrt[12];
t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@
Sort[t[n], Less]], {n, 1, 20}]] (* A194902 *)
TableForm[Table[Flatten[(Position[t[n], #1] &) /@
Sort[t[n], Less]], {n, 1, 15}]]
row[n_] := Position[f, n];
u = TableForm[Table[row[n], {n, 1, 20}]]
g[n_, k_] := Part[row[n], k];
p = Flatten[Table[g[k, n - k + 1], {n, 1, 13},
{k, 1, n}]] (* A194903 *)
q[n_] := Position[p, n]; Flatten[Table[q[n],
{n, 1, 80}]]  (* A194904 *)

Crossrefs

Cf. A194832, A194903, A194904.

Sequence in context: A035458 A259771 A357457 * A194874 A194835 A054065

Adjacent sequences: A194899 A194900 A194901 * A194903 A194904 A194905

Keyword

nonn,tabl

Author

Clark Kimberling, Sep 05 2011

Status

approved