A305570 Number of diagonal Latin squares of order n with the first row in order and at least one orthogonal diagonal mate.

1, 0, 0, 2, 4, 0, 256, 632064, 95024976

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).

Eduard 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) = A305571(n) / n!.

a(n) = A274171(n) - A305568(n).

Crossrefs

Cf. A274171, A305568, A305571, A330391.

Sequence in context: A009512 A317411 A309598 * A287651 A365951 A163259

Adjacent sequences: A305567 A305568 A305569 * A305571 A305572 A305573

Keyword

nonn,more,hard

Author

Eduard I. Vatutin, Jun 05 2018

Extensions

Name clarified by Andrew Howroyd, Oct 19 2020

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

Status

approved