OFFSET
1,4
COMMENTS
a(n) <= 2^m * m! * 4, where m = floor(n/2).
It seems that a(n) = 2^m * m! * 4 for all n > 6. - Eduard I. Vatutin, Jun 08 2020
0 <= A299783(n) <= a(n). - Eduard I. Vatutin, Jun 08 2020
LINKS
E. Vatutin, A. Belyshev, S. Kochemazov, O. Zaikin, N. Nikitina, Enumeration of isotopy classes of diagonal Latin squares of small order using volunteer computing, Supercomputing Days Russia 2018, Moscow, Moscow State University, 2018, pp. 933-942.
E. Vatutin, A. Belyshev, S. Kochemazov, O. Zaikin, N. Nikitina, Enumeration of isotopy classes of diagonal Latin squares of small order using volunteer computing, Communications in Computer and Information Science. Vol. 965. Springer, 2018. pp. 578-586.
E. I. Vatutin, Discussion about properties of diagonal Latin squares (in Russian).
E. I. Vatutin, About the maximal size of main class for diagonal Latin squares of orders 11-15 (in Russian).
Eduard I. Vatutin, Estimating the maximal size of main class for diagonal Latin squares of orders 9-15, Medical-Ecological and Information Technologies - 2020, Part 2, 2020, pp. 57-62. (in Russian)
Eduard I. Vatutin, About the relationship between the minimal and maximal cardinality of main classes for diagonal Latin squares (in Russian).
Eduard I. Vatutin, Proving list (best known examples).
FORMULA
a(n) = A299787(n) / n!.
From Eduard I. Vatutin, May 30 2021: (Start)
EXAMPLE
From Eduard I. Vatutin, May 30 2021: (Start)
The following DLS of order 9 has a main class with cardinality 1536:
0 1 2 3 4 5 6 7 8
1 2 0 4 8 6 5 3 7
7 4 5 8 0 3 2 6 1
5 8 7 6 1 0 3 2 4
8 0 3 2 7 1 4 5 6
3 7 8 5 6 4 1 0 2
6 3 1 7 5 2 8 4 0
2 6 4 0 3 8 7 1 5
4 5 6 1 2 7 0 8 3
The following DLS of order 10 has a main class with cardinality 15360:
0 1 2 3 4 5 6 7 8 9
1 2 0 4 5 3 9 8 6 7
3 5 6 1 8 7 4 0 9 2
9 4 7 8 3 2 1 6 0 5
2 7 3 0 9 8 5 1 4 6
6 8 5 9 2 4 7 3 1 0
4 6 9 7 0 1 3 2 5 8
7 0 4 6 1 9 8 5 2 3
8 3 1 5 6 0 2 9 7 4
5 9 8 2 7 6 0 4 3 1
(End)
CROSSREFS
KEYWORD
nonn,more,hard
AUTHOR
Eduard I. Vatutin, Jan 21 2019
EXTENSIONS
a(9)-a(10) from Eduard I. Vatutin, Mar 15 2020
a(11)-a(15) from Eduard I. Vatutin, Jun 08 2020
STATUS
approved