A194841 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(3).

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

Offset

1,3

Comments

See A194832 for a general discussion.

Links

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

Example

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

Mathematica

r = -Sqrt[3];
t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@ Sort[t[n], Less]], {n, 1, 20}]]   (* A194841 *)
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}]]    (* A194842 *)
q[n_] := Position[p, n]; Flatten[
 Table[q[n], {n, 1, 80}]]   (* A194843 *)

Crossrefs

Cf. A194832, A194842, A194843.

Sequence in context: A098068 A194070 A195183 * A194911 A194865 A075425

Adjacent sequences: A194838 A194839 A194840 * A194842 A194843 A194844

Keyword

nonn,tabl

Author

Clark Kimberling, Sep 04 2011

Status

approved