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A194856 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(5). 4
1, 2, 1, 3, 2, 1, 4, 3, 2, 1, 4, 3, 2, 1, 5, 4, 3, 2, 6, 1, 5, 4, 3, 7, 2, 6, 1, 5, 4, 8, 3, 7, 2, 6, 1, 5, 4, 8, 3, 7, 2, 6, 1, 5, 9, 4, 8, 3, 7, 2, 6, 10, 1, 5, 9, 4, 8, 3, 7, 11, 2, 6, 10, 1, 5, 9, 4, 8, 12, 3, 7, 11, 2, 6, 10, 1, 5, 9, 4, 8, 12, 3, 7, 11, 2, 6, 10, 1, 5, 9, 13, 4, 8, 12 (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

3 2 1

4 3 2 1

4 3 2 1 5

4 3 2 6 1 5

4 3 7 2 6 1 5

4 8  3 7 2 6 1 5

4 8  3 7 2 6 1 5  9

MATHEMATICA

r = -Sqrt[5];

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

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

Sort[t[n], Less]], {n, 1, 20}]]  (* A194856 *)

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}]]  (* A194857 *)

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

{n, 1, 80}]]  (* A194858 *)

CROSSREFS

Cf. A194832, A194857, A194858.

Sequence in context: A335442 A226247 A233742 * A278703 A088643 A226620

Adjacent sequences:  A194853 A194854 A194855 * A194857 A194858 A194859

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Sep 04 2011

STATUS

approved

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Last modified July 30 08:59 EDT 2021. Contains 346356 sequences. (Running on oeis4.)