Minimum number of 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)=15
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)=133
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
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n=11, a(11)=37851
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)=81926
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 
8 11 10 1 6 0 12 2 3 7 5 4 9 
5 7 9 4 10 2 11 8 1 6 3 12 0 
11 12 3 5 0 4 1 9 7 10 2 6 8 
7 9 8 6 12 11 0 10 5 3 4 1 2 
1 3 5 7 2 8 9 11 4 12 6 0 10 
4 10 6 12 3 1 7 5 9 0 8 2 11 
9 0 4 2 8 6 10 3 12 5 11 7 1 
10 5 11 0 1 7 2 4 6 8 12 9 3 
6 4 12 9 11 10 3 1 0 2 7 8 5 
12 2 0 8 5 9 4 6 10 11 1 3 7 
3 8 1 11 7 12 5 0 2 4 9 10 6 
2 6 7 10 9 3 8 12 11 1 0 5 4 

n=15, a(15)=0
-

n=17, a(17)=94407681
Announcement: https://vk.com/wall162891802_2481, Eduard I. Vatutin, Aug 10 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 8 13 5 11 12 15 14 16 9 10
15 10 5 11 7 0 2 12 16 14 13 9 3 4 1 6 8
16 0 13 8 12 15 4 3 14 10 2 1 11 7 9 5 6
3 16 9 6 14 11 12 15 10 1 7 4 8 2 0 13 5
11 7 15 1 10 9 0 14 5 16 12 13 6 3 8 4 2
10 11 7 12 8 14 1 6 2 13 3 16 5 9 15 0 4
4 6 16 15 11 10 9 2 1 0 14 5 13 8 3 7 12
5 15 4 2 16 3 8 9 11 6 0 10 14 12 13 1 7
8 14 6 9 13 7 3 5 4 12 1 15 2 10 11 16 0
1 8 10 13 0 2 14 4 12 11 16 7 9 5 6 3 15
12 5 3 14 9 4 13 1 15 7 8 6 16 0 10 2 11
13 12 8 16 15 1 10 0 9 4 5 14 7 6 2 11 3
9 13 1 10 6 12 11 16 7 3 4 2 0 15 5 8 14
7 9 12 0 3 13 5 11 6 2 15 8 10 16 4 14 1
14 2 11 7 5 8 16 13 0 15 6 3 4 1 12 10 9
6 4 14 5 2 16 15 10 3 8 9 0 1 11 7 12 13

n=19, a(19)=4614888777
Announcement: https://vk.com/wall162891802_2502, Eduard I. Vatutin, Oct 03 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 1 0 5 6 4 8 12 10 15 16 11 9 13 17 18 7 14 
18 15 16 7 14 2 13 6 17 11 4 8 1 0 10 5 3 9 12 
5 16 17 15 18 11 14 10 7 4 8 9 13 6 0 12 2 1 3 
6 11 0 2 17 3 9 12 16 18 5 15 8 14 4 1 7 10 13 
11 18 7 4 6 8 10 1 0 12 13 5 14 16 9 3 17 2 15 
3 12 11 6 8 4 7 0 9 17 16 13 10 2 15 18 5 14 1 
15 10 14 16 11 12 2 5 13 7 3 17 4 18 6 8 1 0 9 
10 5 3 9 12 13 17 4 1 15 2 14 18 8 7 11 6 16 0 
13 2 5 8 3 18 16 9 4 14 1 12 6 17 11 0 10 15 7 
7 4 10 12 0 17 15 18 11 2 9 1 16 3 8 14 13 6 5 
1 8 12 18 16 15 0 13 6 5 17 10 7 11 2 9 14 3 4 
4 9 18 17 10 0 5 15 14 13 7 6 2 1 3 16 12 8 11 
14 7 13 10 1 9 18 11 15 8 6 4 3 12 16 2 0 5 17 
17 6 9 13 15 14 8 2 5 1 11 3 0 10 18 7 4 12 16 
12 13 15 1 2 16 3 14 18 6 0 7 9 5 17 4 8 11 10 
9 14 6 5 13 7 1 3 2 16 18 0 17 15 12 10 11 4 8 
16 0 8 11 7 1 12 17 10 3 14 18 15 4 5 6 9 13 2 
8 17 4 14 9 10 11 16 3 0 12 2 5 7 1 13 15 18 6 

n=21, a(21)=0
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Oct 03 2023