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A194896 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(8). 4
1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 1, 7, 2, 3, 4, 5, 6, 1, 7, 2, 8, 3, 4, 5, 6, 1, 7, 2, 8, 3, 9, 4, 5, 6, 1, 7, 2, 8, 3, 9, 4, 10, 5, 6, 1, 7, 2, 8, 3, 9, 4, 10, 5, 11, 6, 12, 1, 7, 2, 8, 3, 9, 4, 10, 5, 11, 6, 12, 1, 7, 13, 2, 8, 3, 9, 4, 10, 5, 11, 6, 12, 1, 7 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

See A194832 for a general discussion.

LINKS

Table of n, a(n) for n=1..95.

EXAMPLE

First nine rows:

1

1 2

1 2 3

1 2 3 4

1 2 3 4 5

6 1 2 3 4 5

6 1 7 2 3 4 5

6 1 7 2 8 3 4 5

6 1 7 2 8 3 9 4 5

MATHEMATICA

r = -Sqrt[8];

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

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

Sort[t[n], Less]], {n, 1, 20}]] (* A194896 *)

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}]] (* A194897 *)

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

{n, 1, 80}]] (* A194898 *)

CROSSREFS

Cf. A194832, A194897, A194898.

Sequence in context: A194965 A243712 A256553 * A212721 A222417 A253573

Adjacent sequences: A194893 A194894 A194895 * A194897 A194898 A194899

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Sep 04 2011

STATUS

approved

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Last modified January 30 05:55 EST 2023. Contains 359939 sequences. (Running on oeis4.)