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

1,5

Comments

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

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. 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.

Formula

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

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

Crossrefs

Cf. A274171, A266177, A305569, A305570.

Sequence in context: A141367 A141368 A146555 * A057134 A041495 A188315

Adjacent sequences: A305565 A305566 A305567 * A305569 A305570 A305571

Keyword

nonn,more,hard

Author

Eduard I. Vatutin, Jun 05 2018

Extensions

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

Status

approved