A369380 Number of main classes of diagonal Latin squares containing Dabbaghian-Wu pandiagonal Latin squares of order 2n+1.

1, 0, 0, 1, 0, 0, 8, 0, 0, 18, 0, 0

Offset

1,7

Comments

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

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.

Links

Table of n, a(n) for n=1..12.

Vahid Dabbaghian and Tiankuang Wu, Constructing non-cyclic pandiagonal Latin squares of prime orders, Journal of Discrete Algorithms, Vol. 30, 2015, pp. 70-77, doi: 10.1016/j.jda.2014.12.001.

Index entries for sequences related to Latin squares and rectangles.

Crossrefs

Cf. A338562, A342306, A368027, A369379.

Sequence in context: A271407 A347801 A028593 * A037216 A341807 A340915

Adjacent sequences: A369377 A369378 A369379 * A369381 A369382 A369383

Keyword

nonn,more

Author

Eduard I. Vatutin, Jan 22 2024

Status

approved