Minimum number of diagonal transversals in an rotated semicyclic diagonal Latin squares of order n, https://oeis.org/Axxxxxx

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
4 2 3 0 1
3 4 1 2 0
1 3 0 4 2
2 0 4 1 3

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
4 2 6 0 5 1 3
3 5 1 6 0 4 2
5 6 3 4 1 2 0
6 4 5 2 3 0 1
1 3 0 5 2 6 4
2 0 4 1 6 3 5

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)=8795
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 6 10 11 7 2 9 12 5 0 1 8 
5 11 7 9 1 8 12 10 0 3 2 4 6 
9 2 8 12 0 6 5 3 1 4 11 10 7 
12 0 10 5 3 4 9 2 11 6 7 8 1 
6 3 4 1 2 11 7 0 10 8 9 12 5 
2 9 11 7 6 10 8 12 4 1 5 0 3 
11 10 0 8 12 9 1 5 3 7 6 2 4 
7 8 1 4 5 3 0 6 2 11 12 9 10 
1 12 5 6 7 2 11 4 9 10 8 3 0 
4 6 3 2 9 12 10 8 7 0 1 5 11 
8 7 9 11 10 0 3 1 5 12 4 6 2 
10 5 12 0 8 1 4 11 6 2 3 7 9 

n=15, a(15)=0
-

n=17, a(17)=11839718
Announcement: https://vk.com/wall162891802_2472, Eduard I. Vatutin, Aug 04 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 0 4 1 6 7 16 5 15 12 9 13 14 11 8 10
8 11 6 9 16 13 0 2 7 5 14 12 4 1 10 3 15
14 0 12 10 15 11 8 4 6 1 13 2 16 5 7 9 3
3 14 5 7 13 1 9 15 12 4 11 16 2 0 6 10 8
10 13 7 5 12 15 16 3 14 8 4 1 11 9 0 2 6
9 16 8 1 11 14 5 0 4 12 6 15 3 10 2 7 13
11 9 16 15 10 12 13 1 0 14 2 3 5 8 4 6 7
13 2 9 16 6 8 10 14 11 3 0 7 1 15 5 4 12
15 6 3 13 5 16 4 12 2 7 8 10 0 11 9 14 1
6 8 4 2 14 7 3 10 1 11 9 0 15 12 16 13 5
1 10 11 12 0 9 2 13 3 16 15 14 6 7 8 5 4
5 12 1 11 7 3 15 9 10 2 16 4 8 6 13 0 14
16 5 15 0 3 2 12 6 13 10 7 8 14 4 1 11 9
7 4 13 6 2 10 14 8 15 0 3 5 9 16 12 1 11
12 15 10 14 8 4 1 11 9 13 5 6 7 2 3 16 0
4 7 14 8 9 0 11 5 16 6 1 13 10 3 15 12 2

n=19, a(19)=569820165
Announcement: https://vk.com/wall162891802_2494, Eduard I. Vatutin, Sep 04 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 0 4 5 6 7 8 9 10 11 12 13 14 15 17 18 1 16
17 5 9 10 11 14 4 0 15 8 2 18 7 16 12 13 6 3 1
11 0 6 8 16 13 17 18 4 7 14 15 2 12 3 5 1 9 10
10 15 4 18 14 11 2 17 0 3 1 13 9 7 16 12 5 8 6
18 13 16 1 2 10 9 11 3 4 5 14 17 0 6 7 8 12 15
12 18 15 5 9 17 1 10 7 16 3 6 14 4 11 8 2 0 13
6 16 18 11 8 15 5 13 17 0 12 9 1 3 10 14 4 2 7
5 14 7 17 6 18 13 12 16 2 8 1 11 15 9 0 3 10 4
1 17 13 6 7 0 12 2 18 11 4 16 15 5 8 9 10 14 3
16 8 12 15 18 9 0 3 2 14 7 10 5 1 4 6 17 13 11
14 4 8 2 12 3 11 15 10 13 6 5 0 18 1 16 9 7 17
13 11 14 7 0 12 10 6 1 17 16 3 18 8 5 2 15 4 9
9 10 1 14 17 7 18 4 5 12 15 2 3 6 0 11 13 16 8
7 2 5 9 3 8 15 16 6 1 13 0 4 11 17 10 14 18 12
8 6 3 13 15 1 14 9 12 5 18 17 16 10 2 4 7 11 0
15 9 17 16 10 4 8 1 11 18 0 7 6 2 13 3 12 5 14
3 12 10 0 1 2 16 14 13 6 9 4 8 17 7 18 11 15 5
4 7 11 12 13 16 3 5 14 15 17 8 10 9 18 1 0 6 2

n=21, a(21)=0
-

Sep 04 2023