Minimum number of transversals in Brown's diagonal Latin squares of order N=2n, https://oeis.org/Axxxxxx

n=2, a(2)=0
Announcement: https://vk.com/wall162891802_2895, Eduard I. Vatutin, Dec 16 2024
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n=4, a(4)=8
Announcement: https://vk.com/wall162891802_2895, Eduard I. Vatutin, Dec 16 2024
Way of finding: brute force
0 1 2 3 
2 3 0 1 
3 2 1 0 
1 0 3 2 

n=6, a(6)=32
Announcement: https://vk.com/wall162891802_2895, Eduard I. Vatutin, Dec 16 2024
Way of finding: brute force
0 1 2 3 4 5 
1 2 0 5 3 4 
4 3 5 0 2 1 
3 0 1 4 5 2 
5 4 3 2 1 0 
2 5 4 1 0 3 

n=8, a(8)=128
Announcement: https://vk.com/wall162891802_2895, Eduard I. Vatutin, Dec 16 2024
Way of finding: brute force
0 1 2 3 4 5 6 7 
1 2 3 0 5 7 4 6 
5 4 6 7 0 1 3 2 
7 6 4 5 3 2 0 1 
4 5 7 6 1 0 2 3 
6 7 5 4 2 3 1 0 
3 0 1 2 6 4 7 5 
2 3 0 1 7 6 5 4 

n=10, a(10)<=256
Announcement: -, Eduard I. Vatutin, Dec 16 2024
Way of finding: random search, from experiments with spectra
0 1 2 3 4 5 6 7 8 9 
1 5 6 9 2 7 0 3 4 8 
9 8 7 6 5 4 3 2 1 0 
3 2 9 4 8 1 5 0 7 6 
6 7 0 5 1 8 4 9 2 3 
5 9 8 2 3 6 7 1 0 4 
8 4 3 0 7 2 9 6 5 1 
4 0 1 7 6 3 2 8 9 5 
2 6 4 1 9 0 8 5 3 7 
7 3 5 8 0 9 1 4 6 2 

n=12, a(12)<=9984
Announcement: -, Eduard I. Vatutin, May 22 2022
Way of finding: random search, from experiments with spectra
0 1 2 3 4 5 6 7 8 9 10 11 
1 2 0 4 5 3 8 6 7 11 9 10 
2 3 7 5 0 10 1 11 6 4 8 9 
4 8 9 6 11 1 5 0 10 7 3 2 
3 9 10 0 1 2 4 5 11 6 7 8 
5 4 11 7 6 8 3 10 9 0 2 1 
9 10 3 1 2 0 11 4 5 8 6 7 
11 5 4 8 7 6 10 9 3 2 1 0 
10 0 5 2 3 7 9 8 4 1 11 6 
6 11 1 9 8 4 7 3 2 10 0 5 
7 6 8 10 9 11 0 2 1 3 5 4 
8 7 6 11 10 9 2 1 0 5 4 3 

n=14, a(14)<=190976
Announcement: -, Eduard I. Vatutin, Sep 22 2024
Way of finding: random search, from experiments with spectra
0 1 2 3 4 5 6 7 8 9 10 11 12 13 
8 7 1 13 11 9 3 10 4 2 0 12 6 5 
6 3 9 11 8 1 0 13 12 5 2 4 10 7 
10 4 6 8 13 11 12 1 2 0 5 7 9 3 
11 5 13 1 10 6 4 9 7 3 12 0 8 2 
7 10 4 2 5 12 13 0 1 8 11 9 3 6 
1 2 10 9 6 13 5 8 0 7 4 3 11 12 
5 6 12 0 2 4 10 3 9 11 13 1 7 8 
3 9 7 5 0 2 1 12 11 13 8 6 4 10 
12 11 3 4 7 0 8 5 13 6 9 10 2 1 
2 8 0 12 3 7 9 4 6 10 1 13 5 11 
13 12 11 10 9 8 7 6 5 4 3 2 1 0 
4 0 8 6 1 10 2 11 3 12 7 5 13 9 
9 13 5 7 12 3 11 2 10 1 6 8 0 4 

n=16, a(16)<=244744192
Announcement: -, Eduard I. Vatutin, Dec 16 2024
Way of finding: composite squares method
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 
2 3 0 1 5 4 7 6 9 8 11 10 14 15 12 13 
3 2 1 0 6 7 4 5 10 11 8 9 15 14 13 12 
1 0 3 2 7 6 5 4 11 10 9 8 13 12 15 14 
8 11 9 10 14 12 13 15 0 2 3 1 5 6 4 7 
10 9 11 8 13 15 14 12 3 1 0 2 7 4 6 5 
11 8 10 9 15 13 12 14 1 3 2 0 6 5 7 4 
9 10 8 11 12 14 15 13 2 0 1 3 4 7 5 6 
14 15 12 13 8 9 10 11 4 5 6 7 2 3 0 1 
13 12 15 14 10 11 8 9 6 7 4 5 1 0 3 2 
15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 
12 13 14 15 9 8 11 10 5 4 7 6 0 1 2 3 
6 5 7 4 3 1 0 2 13 15 14 12 11 8 10 9 
7 4 6 5 1 3 2 0 15 13 12 14 10 9 11 8 
4 7 5 6 0 2 3 1 14 12 13 15 9 10 8 11 
5 6 4 7 2 0 1 3 12 14 15 13 8 11 9 10 

Dec 22 2024