Minimum number of diagonal transversals in a semicyclic diagonal Latin squares of order n, https://oeis.org/A366332

n=1, a(1)=0
Announcement: https://vk.com/wall162891802_2443, Eduard I. Vatutin, Jul 11 2023
Way of finding: Brute Force + DLX
0

n=3, a(3)=0
-

n=5, a(5)=5
Announcement: https://vk.com/wall162891802_2443, Eduard I. Vatutin, Jul 11 2023
Way of finding: Brute Force + 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=7, a(7)=27
Announcement: https://vk.com/wall162891802_2443, Eduard I. Vatutin, Jul 11 2023
Way of finding: Brute Force + DLX
0 1 2 3 4 5 6 
2 3 4 5 6 0 1 
4 5 6 0 1 2 3 
6 0 1 2 3 4 5 
1 2 3 4 5 6 0 
3 4 5 6 0 1 2 
5 6 0 1 2 3 4 

n=9, a(9)=0
-

n=11, a(11)=4523
Announcement: https://vk.com/wall162891802_2443, Eduard I. Vatutin, Jul 11 2023
Way of finding: Brute Force + DLX
0 1 2 3 4 5 6 7 8 9 10 
2 3 4 5 6 7 8 9 10 0 1 
4 5 6 7 8 9 10 0 1 2 3 
6 7 8 9 10 0 1 2 3 4 5 
8 9 10 0 1 2 3 4 5 6 7 
10 0 1 2 3 4 5 6 7 8 9 
1 2 3 4 5 6 7 8 9 10 0 
3 4 5 6 7 8 9 10 0 1 2 
5 6 7 8 9 10 0 1 2 3 4 
7 8 9 10 0 1 2 3 4 5 6 
9 10 0 1 2 3 4 5 6 7 8 

n=13, a(13)=127339
Announcement: https://vk.com/wall162891802_2443, Eduard I. Vatutin, Jul 11 2023
Way of finding: Brute Force + DLX
0 1 2 3 4 5 6 7 8 9 10 11 12 
3 4 5 6 7 8 9 10 11 12 0 1 2 
8 9 10 11 12 0 1 2 3 4 5 6 7 
4 5 6 7 8 9 10 11 12 0 1 2 3 
12 0 1 2 3 4 5 6 7 8 9 10 11 
9 10 11 12 0 1 2 3 4 5 6 7 8 
5 6 7 8 9 10 11 12 0 1 2 3 4 
1 2 3 4 5 6 7 8 9 10 11 12 0 
11 12 0 1 2 3 4 5 6 7 8 9 10 
6 7 8 9 10 11 12 0 1 2 3 4 5 
2 3 4 5 6 7 8 9 10 11 12 0 1 
7 8 9 10 11 12 0 1 2 3 4 5 6 
10 11 12 0 1 2 3 4 5 6 7 8 9 

n=15, a(15)=0
-

n=17, a(17)=204330233
Announcement: https://vk.com/wall162891802_2450, Eduard I. Vatutin, Jul 21 2023
Way of finding: Brute Force + DLX
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 
2 3 4 5 1 6 7 8 9 10 11 13 14 15 16 12 0 
6 9 7 10 8 11 13 15 12 14 16 0 1 2 3 4 5 
7 10 8 11 9 13 15 12 14 16 0 2 3 4 5 1 6 
13 14 15 16 12 0 2 4 1 3 5 6 9 7 10 8 11 
15 16 12 0 14 2 4 1 3 5 6 7 10 8 11 9 13 
4 5 1 6 3 7 8 9 10 11 13 15 16 12 0 14 2 
8 11 9 13 10 15 12 14 16 0 2 4 5 1 6 3 7 
12 0 14 2 16 4 1 3 5 6 7 8 11 9 13 10 15 
1 6 3 7 5 8 9 10 11 13 15 12 0 14 2 16 4 
9 13 10 15 11 12 14 16 0 2 4 1 6 3 7 5 8 
14 2 16 4 0 1 3 5 6 7 8 9 13 10 15 11 12 
16 4 0 1 2 3 5 6 7 8 9 10 15 11 12 13 14 
3 7 5 8 6 9 10 11 13 15 12 14 2 16 4 0 1 
5 8 6 9 7 10 11 13 15 12 14 16 4 0 1 2 3 
10 15 11 12 13 14 16 0 2 4 1 3 7 5 8 6 9 
11 12 13 14 15 16 0 2 4 1 3 5 8 6 9 7 10 

n=19, a(19)=11232045257
Announcement: https://vk.com/wall162891802_2453, Eduard I. Vatutin, Jul 25 2023
Way of finding: Brute Force + DLX
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 
2 3 4 5 1 6 7 8 9 10 11 12 13 15 16 17 18 14 0 
13 14 15 16 17 18 0 2 4 1 3 5 6 7 10 8 11 9 12 
15 16 17 18 14 0 2 4 1 3 5 6 7 8 11 9 12 10 13 
7 10 8 11 9 12 13 15 17 14 16 18 0 2 3 4 5 1 6 
8 11 9 12 10 13 15 17 14 16 18 0 2 4 5 1 6 3 7 
4 5 1 6 3 7 8 9 10 11 12 13 15 17 18 14 0 16 2 
17 18 14 0 16 2 4 1 3 5 6 7 8 9 12 10 13 11 15 
9 12 10 13 11 15 17 14 16 18 0 2 4 1 6 3 7 5 8 
1 6 3 7 5 8 9 10 11 12 13 15 17 14 0 16 2 18 4 
14 0 16 2 18 4 1 3 5 6 7 8 9 10 13 11 15 12 17 
10 13 11 15 12 17 14 16 18 0 2 4 1 3 7 5 8 6 9 
3 7 5 8 6 9 10 11 12 13 15 17 14 16 2 18 4 0 1 
16 2 18 4 0 1 3 5 6 7 8 9 10 11 15 12 17 13 14 
18 4 0 1 2 3 5 6 7 8 9 10 11 12 17 13 14 15 16 
11 15 12 17 13 14 16 18 0 2 4 1 3 5 8 6 9 7 10 
12 17 13 14 15 16 18 0 2 4 1 3 5 6 9 7 10 8 11 
5 8 6 9 7 10 11 12 13 15 17 14 16 18 4 0 1 2 3 
6 9 7 10 8 11 12 13 15 17 14 16 18 0 1 2 3 4 5 

n=21, a(21)=0
-

Jul 25 2023