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A194868 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=-(1+sqrt(3))/2. 4
1, 2, 1, 2, 1, 3, 2, 4, 1, 3, 5, 2, 4, 1, 3, 5, 2, 4, 1, 6, 3, 5, 2, 7, 4, 1, 6, 3, 8, 5, 2, 7, 4, 1, 6, 3, 8, 5, 2, 7, 4, 1, 9, 6, 3, 8, 5, 2, 10, 7, 4, 1, 9, 6, 3, 8, 5, 2, 10, 7, 4, 1, 9, 6, 3, 11, 8, 5, 2, 10, 7, 4, 12, 1, 9, 6, 3, 11, 8, 5, 13, 2, 10, 7, 4, 12, 1, 9, 6, 3, 11, 8, 5, 13 (list; table; graph; refs; listen; history; text; internal format)
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

5 2 4 1 3

5 2 4 1 6 3

5 2 7 4 1 6 3

8 5 2 7 4 1 6 3

8 5 2 7 4 1 9 6 3

MATHEMATICA

r = -(1 + Sqrt[3])/2;

t[n_] := Table[FractionalPart[k*r], {k, 1, n}];

f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@

Sort[t[n], Less]], {n, 1, 20}]]  (* A194868 *)

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}]] (* A194869 *)

q[n_] := Position[p, n]; Flatten[Table[q[n],

{n, 1, 80}]]   (* A194870 *)

CROSSREFS

Cf. A194832, A194869, A194870.

Sequence in context: A194874 A194835 A054065 * A304574 A139024 A217317

Adjacent sequences:  A194865 A194866 A194867 * A194869 A194870 A194871

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Sep 04 2011

STATUS

approved

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Last modified May 19 18:35 EDT 2022. Contains 353847 sequences. (Running on oeis4.)