A308831 Start with generation 0, which is the empty sequence. For generation N>=1, extend the existing sequence into a non-cyclic ternary de Bruijn sequence of order N. If more than one extension is possible, choose the lexicographically earliest.

0, 1, 2, 0, 0, 2, 2, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 2, 1, 0, 2, 0, 2, 1, 2, 2, 2, 0, 1, 0, 0, 1, 1, 0, 1, 0, 2, 1, 0, 0, 2, 0, 0, 0, 0, 2, 1, 1, 1, 1, 0, 2, 2, 0, 0, 1, 2, 1, 1, 2, 0, 1, 1, 2, 2, 0, 2, 0, 1, 2, 2, 1, 2, 1, 2, 0, 2, 2, 2, 2, 1, 0, 1, 2

Offset

0,3

Comments

If using a binary alphabet instead, it would not be possible to extend the sequence infinitely as a de Bruijn sequence (order 3 needs an extra term: 01100010111). - A. D. Skovgaard, Apr 19 2020

Links

A. D. Skovgaard, Table of n, a(n) for n = 0..246

A. D. Skovgaard, Python program to generate the sequence, with explanatory comments

A. D. Skovgaard, a(n) for n = 0..246 in compressed notation

Example

Generation 1:
[012] (All ternary sequences of length 1 now appear. With 3! = 6 solutions, the lexicographically earliest is chosen.)
Generation 2:
[0120022110] (The sequence is extended from the previous generation, now including all ternary sequences of length 2.)
The process continues.

Crossrefs

Cf. A080679 (binary equivalent), A166315, A169676.

Sequence in context: A107502 A230419 A146165 * A277327 A277328 A318178

Adjacent sequences: A308828 A308829 A308830 * A308832 A308833 A308834

Keyword

nonn

Author

A. D. Skovgaard, Jun 27 2019

Status

approved