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A279649 Rows of the self-orthogonal Latin squares of order 8, lexicographically sorted. 5
1, 2, 3, 4, 5, 6, 7, 8, 3, 4, 1, 2, 6, 5, 8, 7, 4, 5, 7, 3, 8, 2, 1, 6, 6, 7, 5, 8, 3, 1, 2, 4, 7, 1, 4, 6, 2, 8, 5, 3, 5, 8, 6, 7, 1, 3, 4, 2, 8, 3, 2, 5, 4, 7, 6, 1, 2, 6, 8, 1, 7, 4, 3, 5, 1, 2, 3, 4, 5, 6, 7, 8, 3, 4, 1, 2, 6, 5, 8, 7, 4, 5, 8, 3, 7, 2, 6, 1, 6, 8, 5, 7, 3, 1, 4, 2, 8, 1, 4, 6, 2, 7, 3, 5, 5, 7, 6, 8, 1, 3, 2, 4, 2, 6, 7, 1, 8, 4, 5, 3, 7, 3, 2, 5, 4, 8, 1, 6 (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 4180377600 self-orthogonal Latin squares of order 8.

LINKS

Colin Barker, Table of n, a(n) for n = 1..750

Eric Weisstein's World of Mathematics, Latin square

Wikipedia, Latin square

EXAMPLE

The first four squares are:

1 2 3 4 5 6 7 8   1 2 3 4 5 6 7 8   1 2 3 4 5 6 7 8   1 2 3 4 5 6 7 8

3 4 1 2 6 5 8 7   3 4 1 2 6 5 8 7   3 4 1 2 6 5 8 7   3 4 1 2 6 5 8 7

4 5 7 3 8 2 1 6   4 5 8 3 7 2 6 1   4 6 7 3 2 8 1 5   4 6 8 3 2 7 5 1

6 7 5 8 3 1 2 4   6 8 5 7 3 1 4 2   5 7 6 8 1 3 2 4   5 8 6 7 1 3 4 2

7 1 4 6 2 8 5 3   8 1 4 6 2 7 3 5   6 8 5 7 3 1 4 2   6 7 5 8 3 1 2 4

5 8 6 7 1 3 4 2   5 7 6 8 1 3 2 4   7 1 4 5 8 2 6 3   8 1 4 5 7 2 3 6

8 3 2 5 4 7 6 1   2 6 7 1 8 4 5 3   8 3 2 6 7 4 5 1   2 5 7 1 4 8 6 3

2 6 8 1 7 4 3 5   7 3 2 5 4 8 1 6   2 5 8 1 4 7 3 6   7 3 2 6 8 4 1 5

CROSSREFS

Cf. A160368, A279648, A279650, A279849, A279850.

Sequence in context: A245345 A043268 A238593 * A278060 A160597 A282779

Adjacent sequences:  A279646 A279647 A279648 * A279650 A279651 A279652

KEYWORD

nonn,fini,tabf

AUTHOR

Colin Barker, Dec 16 2016

STATUS

approved

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Last modified October 21 18:11 EDT 2018. Contains 316427 sequences. (Running on oeis4.)