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

n=1, a(1)=0
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)=12
Announcement: https://vk.com/wall162891802_2937, Eduard I. Vatutin, Jan 31 2025
Way of finding: brute force
0 1 2 3
3 2 1 0
1 0 3 2
2 3 0 1

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

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

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

Jan 31 2025