

A345370


a(n) is the number of distinct numbers of diagonal transversals that a diagonal Latin square of order n can have.


7




OFFSET

1,5


COMMENTS

a(10) >= 736, a(11) >= 1242, a(12) >= 17693, a(13) >= 14017, a(14) >= 281067, a(15) >= 1958394, a(16) >= 13715.  Eduard I. Vatutin, Oct 29 2021, updated May 14 2023


LINKS

Eduard I. Vatutin, Proving lists (1, 4, 5, 6, 7, 8, 9, 10, 11, 12).
E. I. Vatutin, N. N. Nikitina, M. O. Manzuk, I. I. Kurochkin, A. M. Albertyan, A. V. Kripachev, A. I. Pykhtin, Methods for getting spectra of fast computable numerical characteristics of diagonal Latin squares, Cloud and distributed computing systems in electronic control conference, within the National supercomputing forum (NSCF  2022). PereslavlZalessky, 2023. pp. 1923. (in Russian)
E. I. Vatutin, V. S. Titov, A. I. Pykhtin, A. V. Kripachev, N. N. Nikitina, M. O. Manzuk, A. M. Albertyan, I. I. Kurochkin, Heuristic method for getting approximations of spectra of numerical characteristics for diagonal Latin squares, Intellectual information systems: trends, problems, prospects, Kursk, 2022. pp. 3541. (in Russian)


EXAMPLE

For n=7 the number of diagonal transversals that a diagonal Latin square of order 7 may have is 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, or 27. Since there are 14 distinct values, a(7)=14.


CROSSREFS



KEYWORD

nonn,more,hard


AUTHOR



EXTENSIONS



STATUS

approved



