A279849 Rows of the 48 self-orthogonal Latin squares of order 4, lexicographically sorted.

1, 2, 3, 4, 3, 4, 1, 2, 4, 3, 2, 1, 2, 1, 4, 3, 1, 2, 3, 4, 4, 3, 2, 1, 2, 1, 4, 3, 3, 4, 1, 2, 1, 2, 4, 3, 3, 4, 2, 1, 2, 1, 3, 4, 4, 3, 1, 2, 1, 2, 4, 3, 4, 3, 1, 2, 3, 4, 2, 1, 2, 1, 3, 4, 1, 3, 2, 4, 2, 4, 1, 3, 4, 2, 3, 1, 3, 1, 4, 2, 1, 3, 2, 4, 4, 2, 3, 1, 3, 1, 4, 2, 2, 4, 1, 3

Offset

1,2

Comments

An m X m Latin square consists of m sets of the numbers 1 to m arranged in such a way that no row or column contains the same number twice.

Two m X m Latin squares are orthogonal if no pair of corresponding elements occurs more than once.

A self-orthogonal Latin square is a Latin square that is orthogonal to its transpose.

Links

Colin Barker, Table of n, a(n) for n = 1..768

Eric Weisstein's World of Mathematics, Latin square

Wikipedia, Latin square

Example

The first few squares are:
1 2 3 4   1 2 3 4   1 2 4 3   1 2 4 3   1 3 2 4   1 3 2 4   1 3 4 2
3 4 1 2   4 3 2 1   3 4 2 1   4 3 1 2   2 4 1 3   4 2 3 1   2 4 3 1
4 3 2 1   2 1 4 3   2 1 3 4   3 4 2 1   4 2 3 1   3 1 4 2   3 1 2 4
2 1 4 3   3 4 1 2   4 3 1 2   2 1 3 4   3 1 4 2   2 4 1 3   4 2 1 3

Crossrefs

Cf. A160368, A279648, A279649, A279650, A279850.

Sequence in context: A234347 A328314 A286245 * A106826 A259582 A139048

Adjacent sequences: A279846 A279847 A279848 * A279850 A279851 A279852

Keyword

nonn,fini,full,tabf

Author

Colin Barker, Dec 20 2016

Status

approved