A356924 Irregular table read by rows: invertible bracelets 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 bracelet 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, (2) reversing one string results in the other, or (3) swapping the 0s and 1s in one string results in the other.

There are A000011(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,
  ...

Crossrefs

Cf. A000011.

Cf. A356921 (necklaces), A356922 (bracelets), A356923 (invertible necklaces).

Sequence in context: A219463 A286688 A356923 * A285125 A221152 A302048

Adjacent sequences: A356921 A356922 A356923 * A356925 A356926 A356927

Keyword

nonn,tabf

Author

Peter Kagey, Sep 05 2022

Status

approved