

A098280


Fronttoback insertionpermutation sequence; contains every finite sequence of distinct positive integers.


2



1, 2, 1, 1, 2, 3, 2, 1, 2, 3, 1, 2, 1, 3, 3, 1, 2, 1, 3, 2, 1, 2, 3, 4, 3, 2, 1, 3, 4, 2, 1, 3, 2, 4, 1, 3, 2, 1, 4, 4, 2, 3, 1, 2, 4, 3, 1, 2, 3, 4, 1, 2, 3, 1, 4, 4, 2, 1, 3, 2, 4, 1, 3, 2, 1, 4, 3, 2, 1, 3, 4, 4, 3, 1, 2, 3, 4, 1, 2, 3, 1, 4, 2, 3, 1, 2, 4, 4, 1, 3, 2, 1, 4, 3, 2, 1, 3, 4, 2, 1, 3, 2, 4, 4, 1
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OFFSET

1,2


COMMENTS

Contains every finite sequence of distinct numbers...infinitely many times.


LINKS

Table of n, a(n) for n=1..105.


FORMULA

Write 1. Then place 2 before 1 and then 2 after 1, yielding 21 and 12, as well as the first 5 terms of the sequence. Next, generate the 6 permutations of 1, 2, 3 by inserting 3 into 21 and then 12, from fronttoback, like this: 321, 231, 213 then 213, 132, 123. Next, generate the 24 permutations of 1, 2, 3, 4 by inserting 4 into the permutations of 1, 2, 3. Continue forever.


EXAMPLE

The permutations can be written as
1,
21, 12,
321, 231, 213, 312, 132, 123, etc.
Write them in order and insert commas.


CROSSREFS

Cf. A098281, A030298.
Sequence in context: A014600 A165475 A267134 * A005793 A183391 A029346
Adjacent sequences: A098277 A098278 A098279 * A098281 A098282 A098283


KEYWORD

nonn


AUTHOR

Clark Kimberling, Sep 01 2004


STATUS

approved



