Maximum number of intercalates in an orthogonal diagonal Latin squares of order n, https://oeis.org/A360223

n=1, a(1)=0
Announcement: https://vk.com/wall162891802_1709, Eduard I. Vatutin, Jul 27 2021
Way of finding: trivial
0

n=2, a(2)=0
-

n=3, a(3)=0
-

n=4, a(4)=12
Announcement: https://vk.com/wall162891802_1709, Eduard I. Vatutin, Jul 27 2021
Way of finding: brute force, Euler-Parker method, DLX
0 1 2 3 
2 3 0 1 
3 2 1 0 
1 0 3 2 

n=5, a(5)=0
Announcement: https://vk.com/wall162891802_1709, Eduard I. Vatutin, Jul 27 2021
Way of finding: brute force, Euler-Parker method, DLX
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
Announcement: https://vk.com/wall162891802_1709, Eduard I. Vatutin, Jul 27 2021
Way of finding: brute force, Euler-Parker method, DLX (for n=6 ODLS does not exist)
-

n=7, a(7)=18
Announcement: https://vk.com/wall162891802_1709, Eduard I. Vatutin, Jul 27 2021
Way of finding: brute force, Euler-Parker method, DLX
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)=112
Announcement: https://vk.com/wall162891802_1709, Eduard I. Vatutin, Jul 27 2021
Way of finding: brute force, Euler-Parker method, DLX
0 1 2 3 4 5 6 7 
2 3 0 1 6 7 4 5 
4 5 6 7 0 1 2 3 
6 7 4 5 2 3 0 1 
3 2 1 0 7 6 5 4 
1 0 3 2 5 4 7 6 
7 6 5 4 3 2 1 0 
5 4 7 6 1 0 3 2 

n=9, a(9)=72
Announcement: https://vk.com/wall162891802_1709, Eduard I. Vatutin, Jul 27 2021
Way of finding: brute force, Euler-Parker method, DLX
0 1 2 3 4 5 6 7 8 
1 2 3 4 0 7 8 5 6 
2 6 8 7 5 4 1 0 3 
7 8 6 5 3 0 2 4 1 
3 4 1 0 7 6 5 8 2 
8 7 5 2 6 1 4 3 0 
5 0 4 6 2 8 3 1 7 
4 3 0 1 8 2 7 6 5 
6 5 7 8 1 3 0 2 4 

n=10, a(10)>=76
Announcement: https://vk.com/wall162891802_2547, Eduard I. Vatutin, Nov 28 2023
Way of finding: search for ODLS in neighborhoods of generalized symmetries, Euler-Parker method, DLX
0 1 2 3 4 5 6 7 8 9
1 2 3 0 6 8 4 9 5 7
6 5 9 1 7 4 0 3 2 8
4 9 5 8 2 0 7 6 3 1
3 6 8 7 5 1 9 2 4 0
9 4 7 2 8 6 5 0 1 3
7 8 1 6 0 2 3 4 9 5
8 7 4 5 9 3 2 1 0 6
5 0 6 4 3 9 1 8 7 2
2 3 0 9 1 7 8 5 6 4

n=11, a(11)>=94
Announcement: https://vk.com/wall162891802_1709, Eduard I. Vatutin, Jul 27 2021
Way of finding: random search of DLS, Euler-Parker method, DLX
0 1 2 3 4 5 6 7 8 9 10 
2 3 0 1 5 6 8 10 9 4 7 
5 6 10 8 0 2 1 9 3 7 4 
10 8 7 9 6 4 3 2 1 0 5 
1 0 9 2 7 8 5 4 10 6 3 
3 9 4 10 2 1 0 6 7 5 8 
8 10 6 7 9 3 4 0 5 2 1 
9 2 1 0 8 7 10 5 4 3 6 
7 4 8 5 1 0 2 3 6 10 9 
4 7 5 6 3 10 9 1 2 8 0 
6 5 3 4 10 9 7 8 0 1 2 

n=12, a(12)>=324
Announcement: https://vk.com/wall162891802_2669, Eduard I. Vatutin, Feb 23 2024
Way of finding: neighborhoods of different special types of LS and DLS, Euler-Parker method, DLX
0 1 2 3 4 5 6 7 8 9 10 11
1 2 0 4 9 7 8 10 11 3 5 6
2 0 1 9 3 10 11 5 6 4 7 8
8 6 11 10 7 9 1 4 0 5 3 2
11 8 6 7 5 4 2 3 1 10 9 0
4 3 9 1 0 11 10 8 7 2 6 5
10 7 5 8 6 2 4 1 3 11 0 9
9 4 3 2 1 8 7 6 5 0 11 10
5 10 7 6 11 0 3 2 9 8 1 4
6 11 8 5 10 3 0 9 2 7 4 1
3 9 4 0 2 6 5 11 10 1 8 7
7 5 10 11 8 1 9 0 4 6 2 3

n=13, a(13)>=26
Announcement: -, Eduard I. Vatutin, Jul 21 2022
Way of finding: random search of DLS, Euler-Parker method, DLX
0 1 2 3 4 5 6 7 8 9 10 11 12 
2 3 0 4 5 11 8 6 9 10 12 7 1 
10 5 12 1 0 9 4 2 6 7 8 3 11 
8 6 3 5 10 7 1 11 12 4 9 0 2 
7 8 1 9 11 10 2 12 3 0 4 6 5 
12 9 7 6 1 8 0 5 2 3 11 10 4 
9 11 5 12 7 2 10 3 0 6 1 4 8 
11 10 4 2 3 1 7 9 5 12 0 8 6 
1 12 11 7 2 6 3 10 4 8 5 9 0 
3 7 8 11 6 4 5 0 10 1 2 12 9 
4 2 9 0 12 3 11 8 7 5 6 1 10 
5 0 6 10 8 12 9 4 1 11 7 2 3 
6 4 10 8 9 0 12 1 11 2 3 5 7 

Feb 23 2024