A305569 Number of bachelor diagonal Latin squares of order n.

0, 0, 0, 0, 480, 92160, 861557760, 300261256888320, 1835082185382168791040

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) = A305568(n) * n!.

a(n) = A274806(n) - A305571(n).

Crossrefs

Cf. A266177, A305568, A305571.

Sequence in context: A107511 A288471 A008410 * A289638 A289744 A287933

Adjacent sequences: A305566 A305567 A305568 * A305570 A305571 A305572

Keyword

nonn,more,hard

Author

Eduard I. Vatutin, Jun 05 2018

Extensions

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

Status

approved