Minimum number of transversals in an extended self-orthogonal diagonal Latin square of order n, https://oeis.org/Axxxxxx

n=1, a(1)=1
Announcement: https://vk.com/wall162891802_2937, Eduard I. Vatutin, Jan 31 2025
Way of finding: brute force
0

n=2, a(2)=0
-

n=3, a(3)=0
-

n=4, a(4)=8
Announcement: https://vk.com/wall162891802_2937, Eduard I. Vatutin, Jan 31 2025
Way of finding: brute force
0 1 2 3 
2 3 0 1 
3 2 1 0 
1 0 3 2 

n=5, a(5)=15
Announcement: https://vk.com/wall162891802_2937, Eduard I. Vatutin, Jan 31 2025
Way of finding: brute force
0 1 2 3 4 
2 3 4 0 1 
4 0 1 2 3 
1 2 3 4 0 
3 4 0 1 2 

n=6, a(6)=0
-

n=7, a(7)=23
Announcement: https://vk.com/wall162891802_2937, Eduard I. Vatutin, Jan 31 2025
Way of finding: brute force
0 1 2 3 4 5 6 
1 2 5 4 6 0 3 
5 3 6 1 2 4 0 
2 6 4 5 0 3 1 
4 0 1 2 3 6 5 
6 4 3 0 5 1 2 
3 5 0 6 1 2 4 

n=8, a(8)=128
Announcement: https://vk.com/wall162891802_2937, Eduard I. Vatutin, Jan 31 2025
Way of finding: brute force
0 1 2 3 4 5 6 7 
1 2 0 4 3 7 5 6 
2 3 7 6 1 0 4 5 
7 4 1 5 2 6 3 0 
3 0 5 1 6 2 7 4 
6 7 3 2 5 4 0 1 
5 6 4 0 7 3 1 2 
4 5 6 7 0 1 2 3 

n=9, a(9)=133
Announcement: https://vk.com/wall162891802_2937, Eduard I. Vatutin, Jan 31 2025
Way of finding: brute force
0 1 2 3 4 5 6 7 8 
1 2 3 5 8 4 0 6 7 
5 3 6 1 0 7 2 8 4 
3 4 0 7 6 1 8 5 2 
6 0 8 4 3 2 7 1 5 
4 6 7 0 5 8 1 2 3 
2 7 4 8 1 0 5 3 6 
8 5 1 2 7 6 3 4 0 
7 8 5 6 2 3 4 0 1 

n=10, a(10)=716
Announcement: https://vk.com/wall162891802_2937, Eduard I. Vatutin, Jan 31 2025
Way of finding: brute force
0 1 2 3 4 5 6 7 8 9 
1 2 0 4 6 8 7 9 3 5 
9 7 8 0 3 1 2 5 4 6 
7 6 9 5 1 4 0 8 2 3 
4 3 1 8 9 6 5 2 0 7 
3 5 6 9 8 7 4 0 1 2 
8 0 5 1 2 9 3 6 7 4 
6 8 7 2 5 3 1 4 9 0 
5 4 3 7 0 2 9 1 6 8 
2 9 4 6 7 0 8 3 5 1 

Jan 31 2025