A098280 Front-to-back insertion-permutation sequence.

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

Offset

1,2

Comments

Contains every finite sequence of distinct numbers infinitely many times.

Links

Table of n, a(n) for n=1..119.

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 front-to-back, 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.

Prog

(PARI) tabf(nn) = my(v=[[1]], w); print(v); for(n=2, nn, w=List([]); for(k=1, #v, for(i=1, n, listput(w, concat([v[k][1..i-1], n, v[k][i..n-1]])))); print(Vec(v=w))); \\ Jinyuan Wang, Sep 01 2021

Crossrefs

Cf. A030298, A098281.

Sequence in context: A341456 A319420 A267134 * A005793 A183391 A029346

Adjacent sequences: A098277 A098278 A098279 * A098281 A098282 A098283

Keyword

nonn

Author

Clark Kimberling, Sep 01 2004

Status

approved