login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A360220 Maximum number of diagonal transversals in an orthogonal diagonal Latin square of order n. 3
1, 0, 0, 4, 5, 0, 27, 120, 333 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
COMMENTS
An orthogonal diagonal Latin square is a diagonal Latin square that has at least one orthogonal diagonal mate.
a(10) >= 866, a(11) >= 4828, a(12) >= 30192, a(13) >= 131106, a(17) >= 204995269, a(19) >= 11254190082.
For most orders n, at least one diagonal Latin square with the maximal number of diagonal transversals has an orthogonal mate and A287648(n) = a(n). Known exceptions: n=6 and n=10. - Eduard I. Vatutin, Feb 17 2023
Every orthogonal diagonal Latin square is a diagonal Latin square, so A287647(n) <= A354068(n) <= a(n) <= A287648(n). - Eduard I. Vatutin, Mar 04 2023
LINKS
E. I. Vatutin, N. N. Nikitina, M. O. Manzuk, A. M. Albertyan, and I. I. Kurochkin, On the construction of spectra of fast-computable numerical characteristics for diagonal Latin squares of small order, Intellectual and Information Systems (Intellect - 2021), Tula, 2021, pp. 7-17. (in Russian)
CROSSREFS
Sequence in context: A178219 A322232 A232397 * A375943 A122753 A016714
KEYWORD
nonn,more,hard
AUTHOR
Eduard I. Vatutin, Jan 30 2023
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 17 05:28 EDT 2024. Contains 375985 sequences. (Running on oeis4.)