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A299784 Maximal size of a main class for diagonal Latin squares of order n with the first row in ascending order. 6
1, 0, 0, 2, 4, 96, 192, 1536, 1536, 15360, 15360, 184320, 184320, 2580480, 2580480 (list; graph; refs; listen; history; text; internal format)
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.
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)
FORMULA
a(n) = A299787(n) / n!.
From Eduard I. Vatutin, May 30 2021: (Start)
A299783(n) = A299784(n) for 1 <= n <= 5.
A299783(6)*3 = A299784(6).
A299783(7)*6 = A299784(7).
A299783(8)*16 = A299784(8).
A299783(9)*32 = A299784(9).
A299783(10)*2 = A299784(10).
A299783(11)*10 = A299784(11).
A299783(12)*4 = A299784(12).
A299783(13)*24 = A299784(13). (End)
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
Sequence in context: A335291 A156496 A007534 * A009379 A092918 A018428
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

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)