Maximum number of diagonal transversals in a cyclic diagonal Latin square of order n, https://oeis.org/A342997

n=1, a(1)=1
Way of finding: brute force
0

n=2, a(2)=0
-

n=3, a(3)=0
-

n=4, a(4)=0
-

n=5, a(5)=1
Announcement: https://vk.com/wall162891802_1412, Eduard I. Vatutin, Oct 28 2020
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)=27
Announcement: https://vk.com/wall162891802_1412, Eduard I. Vatutin, Oct 28 2020
Way of finding: brute force
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=8, a(8)=0
-

n=9, a(9)=0
-

n=10, a(10)=0
-

n=11, a(11)=4665
Announcement: https://vk.com/wall162891802_1412, Eduard I. Vatutin, Oct 28 2020
Way of finding: brute force
0 1 2 3 4 5 6 7 8 9 10
3 4 5 6 7 8 9 10 0 1 2
6 7 8 9 10 0 1 2 3 4 5
9 10 0 1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8 9 10 0
4 5 6 7 8 9 10 0 1 2 3
7 8 9 10 0 1 2 3 4 5 6
10 0 1 2 3 4 5 6 7 8 9
2 3 4 5 6 7 8 9 10 0 1
5 6 7 8 9 10 0 1 2 3 4
8 9 10 0 1 2 3 4 5 6 7

n=12, a(12)=0
-

n=13, a(13)=131106
Announcement: https://vk.com/wall162891802_1412, Eduard I. Vatutin, Oct 28 2020
Way of finding: brute force
0 1 2 3 4 5 6 7 8 9 10 11 12
2 3 4 5 6 7 8 9 10 11 12 0 1
4 5 6 7 8 9 10 11 12 0 1 2 3
6 7 8 9 10 11 12 0 1 2 3 4 5
8 9 10 11 12 0 1 2 3 4 5 6 7
10 11 12 0 1 2 3 4 5 6 7 8 9
12 0 1 2 3 4 5 6 7 8 9 10 11
1 2 3 4 5 6 7 8 9 10 11 12 0
3 4 5 6 7 8 9 10 11 12 0 1 2
5 6 7 8 9 10 11 12 0 1 2 3 4
7 8 9 10 11 12 0 1 2 3 4 5 6
9 10 11 12 0 1 2 3 4 5 6 7 8
11 12 0 1 2 3 4 5 6 7 8 9 10

n=14, a(14)=0
-

n=15, a(15)=0
-

n=16, a(16)=0
-

n=17, a(17)=204995269
Announcement: https://vk.com/wall162891802_1412, Eduard I. Vatutin, Oct 28 2020
Way of finding: brute force
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0 1
4 5 6 7 8 9 10 11 12 13 14 15 16 0 1 2 3
6 7 8 9 10 11 12 13 14 15 16 0 1 2 3 4 5
8 9 10 11 12 13 14 15 16 0 1 2 3 4 5 6 7
10 11 12 13 14 15 16 0 1 2 3 4 5 6 7 8 9
12 13 14 15 16 0 1 2 3 4 5 6 7 8 9 10 11
14 15 16 0 1 2 3 4 5 6 7 8 9 10 11 12 13
16 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0
3 4 5 6 7 8 9 10 11 12 13 14 15 16 0 1 2
5 6 7 8 9 10 11 12 13 14 15 16 0 1 2 3 4
7 8 9 10 11 12 13 14 15 16 0 1 2 3 4 5 6
9 10 11 12 13 14 15 16 0 1 2 3 4 5 6 7 8
11 12 13 14 15 16 0 1 2 3 4 5 6 7 8 9 10
13 14 15 16 0 1 2 3 4 5 6 7 8 9 10 11 12
15 16 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

n=18, a(18)=0
-

n=19, a(19)=11254190082
Announcement: https://vk.com/wall162891802_1412, Eduard I. Vatutin, Oct 28 2020
Way of finding: brute force
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 0 1
4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 0 1 2 3
6 7 8 9 10 11 12 13 14 15 16 17 18 0 1 2 3 4 5
8 9 10 11 12 13 14 15 16 17 18 0 1 2 3 4 5 6 7
10 11 12 13 14 15 16 17 18 0 1 2 3 4 5 6 7 8 9
12 13 14 15 16 17 18 0 1 2 3 4 5 6 7 8 9 10 11
14 15 16 17 18 0 1 2 3 4 5 6 7 8 9 10 11 12 13
16 17 18 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
18 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 0
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 0 1 2
5 6 7 8 9 10 11 12 13 14 15 16 17 18 0 1 2 3 4
7 8 9 10 11 12 13 14 15 16 17 18 0 1 2 3 4 5 6
9 10 11 12 13 14 15 16 17 18 0 1 2 3 4 5 6 7 8
11 12 13 14 15 16 17 18 0 1 2 3 4 5 6 7 8 9 10
13 14 15 16 17 18 0 1 2 3 4 5 6 7 8 9 10 11 12
15 16 17 18 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
17 18 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

n=20, a(20)=0
-

n=21, a(21)=0
-

n=22, a(22)=0
-

Oct 28 2020