Minimum number of diagonal 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)=4
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)=5
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)=8
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 4 5 6 3 0 
6 4 5 2 0 1 3 
5 3 6 4 1 0 2 
4 6 1 0 3 2 5 
3 5 0 1 2 6 4 
2 0 3 6 5 4 1 

n=8, a(8)=16
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 3 0 5 7 4 6 
5 4 6 7 2 3 1 0 
4 6 7 5 1 2 0 3 
7 5 4 6 3 0 2 1 
6 7 5 4 0 1 3 2 
3 0 1 2 6 4 7 5 
2 3 0 1 7 6 5 4 

n=9, a(9)=15
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 7 0 6 8 4 5 
7 0 4 5 8 1 2 3 6 
4 5 7 6 2 0 1 8 3 
5 8 1 4 3 7 0 6 2 
3 6 0 1 5 8 4 2 7 
8 3 5 0 6 2 7 1 4 
2 7 6 8 1 4 3 5 0 
6 4 8 2 7 3 5 0 1 

n=10, a(10)=75
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 7 8 9 6 5 3 
5 7 8 9 2 1 0 4 3 6 
4 6 1 7 5 9 2 3 0 8 
6 5 7 8 9 3 1 0 4 2 
9 4 3 5 0 6 7 8 2 1 
8 0 4 1 6 7 3 2 9 5 
3 9 6 2 1 4 8 5 7 0 
2 8 5 6 3 0 4 9 1 7 
7 3 9 0 8 2 5 1 6 4 

Jan 31 2025