A356923 Irregular table read by rows: invertible necklaces on the alphabet {0,1} sorted by length then by lexicographic order of minimum presentation.

0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0

Offset

1

Comments

An invertible necklace on the alphabet {0,1} is an equivalence class of binary strings where two strings are considered the same if (1) one string can be rotated to form the other or (2) swapping the 0s and 1s in one string results in the other string.

There are A000013(n) rows of length n.

Links

Table of n, a(n) for n=1..87.

Example

Table begins:
  0,
  0, 0,
  0, 1,
  0, 0, 0,
  0, 0, 1,
  0, 0, 0, 0,
  0, 0, 0, 1,
  0, 0, 1, 1,
  0, 1, 0, 1,
  0, 0, 0, 0, 0,
  0, 0, 0, 0, 1,
  0, 0, 0, 1, 1,
  0, 0, 1, 0, 1,
  0, 0, 0, 0, 0, 0,
  0, 0, 0, 0, 0, 1,
  0, 0, 0, 0, 1, 1,
  0, 0, 0, 1, 0, 1,
  0, 0, 0, 1, 1, 1,
  0, 0, 1, 0, 0, 1,
  0, 0, 1, 0, 1, 1,
  0, 1, 0, 1, 0, 1,
  ...
"0,0,1,1,1" is not a a row in this table because 0,0,1,1,1 = 1,1,0,0,0 = 0,0,0,1,1 and 0,0,0,1,1 is lexicographically earlier.

Crossrefs

Cf. A000013.

Cf. A356921 (necklaces), A356922 (bracelets), A356924 (invertible bracelets).

Sequence in context: A350289 A219463 A286688 * A356924 A285125 A221152

Adjacent sequences: A356920 A356921 A356922 * A356924 A356925 A356926

Keyword

nonn,tabf

Author

Peter Kagey, Sep 04 2022

Status

approved