The following files contain an enumeration of all inequivalent Williamson sequences of a given order `n` which is divisible by 2 or 3 under the following equivalence operations:

- Reorder the sequences
`A`,`B`,`C`,`D`in any way. - Negate all the entries in any of
`A`,`B`,`C`, or`D`. - If
`n`is even, cyclically shift all the entries in any of`A`,`B`,`C`, or`D`by an offset of`n`/2. - Apply an automorphism of the cyclic group
`C`_{n}to all the indices of the entries of`A`,`B`,`C`, and`D`simultaneously. - If
`n`is even, negate every second entry in each of`A`,`B`,`C`, and`D`simultaneously.

Every line in each file contains exactly one Williamson sequence, with spaces separating the members `A`, `B`, `C` and `D` of the Williamson sequence. The sequence entries are encoded using the characters + for 1 and - for −1. The sequences were constructed using a SAT+CAS method which is described in the paper Applying Computer Algebra Systems with SAT Solvers to the Williamson Conjecture by Bright, Kotsireas, and Ganesh. They have also been archived on Zenodo.

order n |
# sequences | filesize |

2 | 1 | 12 |

3 | 1 | 16 |

4 | 1 | 20 |

6 | 1 | 28 |

8 | 1 | 36 |

9 | 3 | 120 |

10 | 2 | 88 |

12 | 3 | 156 |

14 | 5 | 300 |

15 | 4 | 256 |

16 | 6 | 408 |

18 | 23 | 1.8K |

20 | 17 | 1.4K |

21 | 7 | 616 |

22 | 15 | 1.4K |

24 | 72 | 7.1K |

26 | 26 | 2.8K |

27 | 6 | 672 |

28 | 83 | 9.5K |

30 | 150 | 19K |

32 | 152 | 20K |

33 | 5 | 680 |

34 | 91 | 13K |

36 | 477 | 69K |

38 | 50 | 7.7K |

39 | 1 | 160 |

40 | 1499 | 241K |

42 | 301 | 51K |

44 | 249 | 44K |

45 | 1 | 184 |

46 | 50 | 9.2K |

48 | 9800 | 1.9M |

50 | 275 | 55K |

51 | 2 | 416 |

52 | 926 | 192K |

54 | 498 | 107K |

56 | 40315 | 8.8M |

57 | 1 | 232 |

58 | 73 | 17K |

60 | 4083 | 973K |

62 | 61 | 16K |

63 | 2 | 512 |

64 | 69960 | 18M |

66 | 262 | 69K |

68 | 1113 | 300K |

69 | 1 | 280 |

70 | 98 | 28K |