A369380 - OEIS

%I #8 Feb 14 2024 14:07:36

%S 1,0,0,1,0,0,8,0,0,18,0,0

%N Number of main classes of diagonal Latin squares containing Dabbaghian-Wu pandiagonal Latin squares of order 2n+1.

%C A pandiagonal Latin square is a Latin square in which the diagonal, antidiagonal and all broken diagonals and antidiagonals are transversals.

%C A Dabbaghian-Wu pandiagonal Latin square (see A368027) is a special type of pandiagonal Latin square (see A342306). Such squares are constructed from cyclic diagonal Latin squares (see A338562) for prime orders n=6k+1 (see Dabbaghian and Wu article) using a polynomial algorithm based on permutation of some values in Latin square. For other orders (25, 35, 49, ...) this algorithm also ensures correct pandiagonal Latin squares.

%H Vahid Dabbaghian and Tiankuang Wu, <a href="https://doi.org/10.1016/j.jda.2014.12.001">Constructing non-cyclic pandiagonal Latin squares of prime orders</a>, Journal of Discrete Algorithms, Vol. 30, 2015, pp. 70-77, doi: 10.1016/j.jda.2014.12.001.

%H <a href="https://oeis.org/index/La#Latin">Index entries for sequences related to Latin squares and rectangles</a>.

%Y Cf. A338562, A342306, A368027, A369379.

%K nonn,more

%O 1,7

%A _Eduard I. Vatutin_, Jan 22 2024