%I
%S 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,
%T 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,
%U 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
%N Rows of the selforthogonal Latin squares of order 7, lexicographically sorted.
%C 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.
%C Two m X m Latin squares are orthogonal if no pair of corresponding elements occurs more than once.
%C A selforthogonal Latin square is a Latin square that is orthogonal to its transpose.
%C There are 19353600 selforthogonal Latin squares of order 7.
%H Colin Barker, <a href="/A279648/b279648.txt">Table of n, a(n) for n = 1..500</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LatinSquare.html">Latin square</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Latin_square">Latin square</a>
%e The first four squares are:
%e 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
%e 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
%e 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
%e 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
%e 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
%e 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
%e 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
%Y Cf. A160368, A279649, A279650, A279849, A279850.
%K nonn,fini,tabf
%O 1,2
%A _Colin Barker_, Dec 16 2016
