A330391 Number of main classes of diagonal Latin squares of order n with at least one orthogonal diagonal mate.

1, 0, 0, 1, 1, 0, 5, 1105, 75307

Offset

1,7

Links

Table of n, a(n) for n=1..9.

Natalia Makarova, Database CF ODLS of order n

E. I. Vatutin, Discussion about properties of diagonal Latin squares (in Russian)

E. I. Vatutin, List of all main classes of orthogonal diagonal Latin squares of orders 1-8.

E. I. Vatutin, List of all main classes of orthogonal diagonal Latin squares of order 9.

E. I. Vatutin, List of known main classes of orthogonal diagonal Latin squares of order 11.

E. I. Vatutin, Special types of diagonal Latin squares, Cloud and distributed computing systems in electronic control conference, within the National supercomputing forum (NSCF - 2022). Pereslavl-Zalessky, 2023. pp. 9-18. (in Russian)

E. Vatutin, A. Belyshev, Enumerating the Orthogonal Diagonal Latin Squares of Small Order for Different Types of Orthogonality, Communications in Computer and Information Science, Vol. 1331, Springer, 2020, pp. 586-597.

Eduard I. Vatutin, Natalia N. Nikitina, and Maxim O. Manzuk, First results of an experiment on studying the properties of DLS of order 9 in the volunteer distributed computing projects Gerasim@Home and RakeSearch (in Russian).

Index entries for sequences related to Latin squares and rectangles.

Formula

a(n) = A287764(n) - A337309(n).

Crossrefs

Cf. A287651, A287764, A287695, A305570, A305571, A337309.

Sequence in context: A220790 A372705 A123266 * A303894 A305286 A304899

Adjacent sequences: A330388 A330389 A330390 * A330392 A330393 A330394

Keyword

nonn,more,hard

Author

Eduard I. Vatutin, Feb 25 2020

Extensions

a(9) added by Eduard I. Vatutin, Dec 12 2020

Status

approved