A305568 Number of bachelor diagonal Latin squares of order n with the first row in ascending order.

0, 0, 0, 0, 4, 128, 170944, 7446955776, 5056994558482608

Offset: 1

Author

Eduard I. Vatutin, Jun 05 2018

Keywords

• nonn
• more
• hard

Comments

A bachelor diagonal Latin square is one with no orthogonal mate.

Links

• 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. I. Vatutin, S. E. Kochemazov, O. S. Zaikin, 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, 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, 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).
• Index entries for sequences related to Latin squares and rectangles.

Crossrefs

Cf. A274171, A266177, A305569, A305570.

Formula

a(n) = A305569(n) / n!.

a(n) = A274171(n) - A305570(n).

Extensions

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