A393633 Triangle giving the number L(k,n) of paratopy classes of (k X n)-Latin rectangles.

1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 2, 3, 3, 2, 1, 4, 14, 44, 33, 12, 1, 4, 45, 808, 3712, 1895, 147, 1, 7, 259, 48295, 2379263, 14610901, 6670346, 283657, 1, 8, 1700, 4028568

Offset

1,8

Comments

The paratopy class is an equivalence class of Latin rectangles. In addition to the operations of row permutation, column permutation and symbol permutation, under paratopy, the roles of "row", "column" and "symbol" can be permuted (when the dimensions match).

References

Patric R. J. Östergård and Luka Tolonen, Classifying Equidistant Permutation Codes (in preparation).

Links

Table of n, a(n) for n=1..40.

Example

Triangle begins:
  1;
  1, 1;
  1, 1, 1;
  1, 2, 2, 2;
  1, 2, 3, 3, 2;
  1, 4, 14, 44, 33, 12;
  1, 4, 45, 808, 3712, 1895, 147;
  1, 7, 259, 48295, 2379263, 14610901, 6670346, 283657;
  1, 8, 1700, 4028568, ...

Crossrefs

Cf. A162544 for the corresponding numbers of isotopy classes.

Sequence in context: A373092 A222656 A162545 * A162544 A209323 A083647

Adjacent sequences: A393630 A393631 A393632 * A393634 A393635 A393636

Keyword

nonn,tabl,more

Author

Luka Tolonen, Feb 23 2026

Status

approved