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A279648 Rows of the self-orthogonal Latin squares of order 7, lexicographically sorted. 5
1, 2, 3, 4, 5, 6, 7, 3, 4, 2, 5, 6, 7, 1, 4, 7, 6, 3, 1, 2, 5, 6, 1, 5, 7, 2, 4, 3, 2, 5, 7, 6, 3, 1, 4, 7, 3, 1, 2, 4, 5, 6, 5, 6, 4, 1, 7, 3, 2, 1, 2, 3, 4, 5, 6, 7, 3, 4, 2, 5, 6, 7, 1, 5, 1, 6, 7, 3, 4, 2, 6, 7, 1, 3, 2, 5, 4, 2, 5, 4, 6, 7, 1, 3, 7, 3, 5, 1, 4, 2, 6, 4, 6, 7, 2, 1, 3, 5 (list; graph; refs; listen; history; text; internal format)
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.

There are 19353600 self-orthogonal Latin squares of order 7.

LINKS

Colin Barker, Table of n, a(n) for n = 1..500

Eric Weisstein's World of Mathematics, Latin square

Wikipedia, Latin square

EXAMPLE

The first four squares are:

1 2 3 4 5 6 7   1 2 3 4 5 6 7   1 2 3 4 5 6 7   1 2 3 4 5 6 7

3 4 2 5 6 7 1   3 4 2 5 6 7 1   3 4 2 5 6 7 1   3 4 2 5 6 7 1

4 7 6 3 1 2 5   5 1 6 7 3 4 2   5 7 6 1 3 2 4   5 7 6 1 3 2 4

6 1 5 7 2 4 3   6 7 1 3 2 5 4   6 1 7 2 4 3 5   6 1 7 3 2 4 5

2 5 7 6 3 1 4   2 5 4 6 7 1 3   2 5 1 3 7 4 6   2 5 4 6 7 1 3

7 3 1 2 4 5 6   7 3 5 1 4 2 6   7 3 4 6 1 5 2   7 3 1 2 4 5 6

5 6 4 1 7 3 2   4 6 7 2 1 3 5   4 6 5 7 2 1 3   4 6 5 7 1 3 2

CROSSREFS

Cf. A160368, A279649, A279650, A279849, A279850.

Sequence in context: A097449 A104415 A071074 * A066323 A245347 A278059

Adjacent sequences:  A279645 A279646 A279647 * A279649 A279650 A279651

KEYWORD

nonn,fini,tabf

AUTHOR

Colin Barker, Dec 16 2016

STATUS

approved

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Last modified April 18 06:48 EDT 2019. Contains 322209 sequences. (Running on oeis4.)