A305571 Number of diagonal Latin squares of order n with at least one orthogonal diagonal mate.

1, 0, 0, 48, 480, 0, 1290240, 25484820480, 34482663290880

Offset

1,4

Links

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

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

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 and 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.

E. I. Vatutin, S. E. Kochemazov, O. S. Zaikin, and I. I. Citerra, Estimation of the probability of finding orthogonal diagonal Latin squares among general diagonal Latin squares, Recognition - 2018. Kursk: SWSU, 2018. pp. 72-74. (in Russian).

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).

Eduard I. Vatutin, Natalia N. Nikitina, and Maxim O. Manzuk, Additional calculated 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).

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

Index entries for sequences related to Latin squares and rectangles.

Formula

a(n) = A305570(n) * n!.

a(n) = A274806(n) - A305569(n).

Crossrefs

Cf. A274806, A305569, A305570.

Sequence in context: A333671 A287762 A309599 * A229505 A299785 A299787

Adjacent sequences: A305568 A305569 A305570 * A305572 A305573 A305574

Keyword

nonn,more,hard

Author

Eduard I. Vatutin, Jun 05 2018

Extensions

a(9) added by Eduard I. Vatutin, Dec 22 2020

Status

approved