Maximum number of transversals in a diagonal Latin square of order n, https://oeis.org/A287644 n=1, a(1)=1 Announcement: https://users.monash.edu.au/~iwanless/data/transversals/, Ian Wanless et al. 0 n=2, a(2)=0 Announcement: https://users.monash.edu.au/~iwanless/data/transversals/, Ian Wanless et al. 0 1 1 0 n=3, a(3)=3 0 1 2 2 0 1 1 2 0 n=4, a(4)=8 Announcement: https://users.monash.edu.au/~iwanless/data/transversals/, Ian Wanless et al. 0 1 2 3 3 2 1 0 1 0 3 2 2 3 0 1 n=5, a(5)=15 Announcement: https://users.monash.edu.au/~iwanless/data/transversals/, Ian Wanless et al. 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=6, a(6)=32 Announcement: https://users.monash.edu.au/~iwanless/data/transversals/, Ian Wanless et al. 0 1 2 3 4 5 4 2 5 0 3 1 3 5 1 2 0 4 5 3 0 4 1 2 2 4 3 1 5 0 1 0 4 5 2 3 n=7, a(7)=133 Announcement: https://users.monash.edu.au/~iwanless/data/transversals/, Ian Wanless et al. 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=8, a(8)=384 Announcement: https://users.monash.edu.au/~iwanless/data/transversals/, Ian Wanless et al. 0 1 2 3 4 5 6 7 1 2 3 0 6 7 5 4 6 5 7 4 1 3 2 0 5 3 4 1 2 0 7 6 2 7 0 6 5 4 3 1 3 4 1 5 7 6 0 2 7 0 6 2 3 1 4 5 4 6 5 7 0 2 1 3 n=9, a(9)=2241 Announcement: https://users.monash.edu.au/~iwanless/data/transversals/, Ian Wanless et al. 0 1 2 3 4 5 6 7 8 7 8 4 0 6 1 2 3 5 4 3 1 2 8 7 5 6 0 1 6 7 5 3 4 0 8 2 5 4 0 8 7 2 3 1 6 8 2 3 1 0 6 7 5 4 3 5 6 7 2 8 4 0 1 6 0 8 4 5 3 1 2 7 2 7 5 6 1 0 8 4 3 n=10, a(10)>=5504 Announcement: https://users.monash.edu.au/~iwanless/data/transversals/, Ian Wanless et al. 0 8 5 1 7 3 4 6 9 2 5 1 7 2 9 8 0 3 4 6 1 7 2 9 5 6 8 0 3 4 9 6 4 3 0 2 7 1 5 8 3 0 8 6 4 1 5 9 2 7 4 3 0 8 6 5 9 2 7 1 7 2 9 5 1 4 6 8 0 3 6 4 3 0 8 9 2 7 1 5 2 9 6 4 3 7 1 5 8 0 8 5 1 7 2 0 3 4 6 9 n=11, a(11)>=37851 Announcement: https://users.monash.edu.au/~iwanless/data/transversals/, Ian Wanless et al. 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=12, a(12)>=198144 Announcement: https://users.monash.edu.au/~iwanless/data/transversals/, Ian Wanless et al. 0 1 2 3 4 5 6 7 8 9 10 11 1 2 3 4 5 0 11 6 7 8 9 10 9 8 7 6 11 10 1 0 5 4 3 2 4 5 0 1 2 3 8 9 10 11 6 7 6 11 10 9 8 7 4 3 2 1 0 5 11 10 9 8 7 6 5 4 3 2 1 0 3 4 5 0 1 2 9 10 11 6 7 8 2 3 4 5 0 1 10 11 6 7 8 9 10 9 8 7 6 11 0 5 4 3 2 1 5 0 1 2 3 4 7 8 9 10 11 6 7 6 11 10 9 8 3 2 1 0 5 4 8 7 6 11 10 9 2 1 0 5 4 3 n=13, a(13)>=1030367 Announcement: https://users.monash.edu.au/~iwanless/data/transversals/, Ian Wanless et al. 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)>=3477504 Announcement: https://users.monash.edu.au/~iwanless/data/transversals/, Ian Wanless et al. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 1 2 3 4 5 6 7 8 9 10 11 12 13 0 2 3 4 5 6 7 8 9 10 11 12 13 0 1 3 4 5 6 7 8 9 10 11 12 13 0 1 2 4 5 6 7 8 9 10 11 12 13 0 1 2 3 5 6 7 8 9 10 11 12 13 0 1 2 3 4 6 7 8 9 10 11 12 13 0 1 2 3 4 5 7 8 9 10 11 12 13 0 1 2 3 4 5 6 8 9 10 11 12 13 0 1 2 3 4 5 6 7 9 10 11 12 13 0 1 2 3 4 5 6 7 8 10 11 12 13 0 1 2 3 4 5 6 7 8 9 11 12 13 0 1 2 3 4 5 6 7 8 9 10 12 13 0 1 2 3 4 5 6 7 8 9 10 11 13 0 1 2 3 4 5 6 7 8 9 10 11 12 n=15, a(15)>=36362925 Announcement: https://users.monash.edu.au/~iwanless/data/transversals/, Ian Wanless et al. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 0 2 3 4 5 6 7 8 9 10 11 12 13 14 0 1 3 4 5 6 7 8 9 10 11 12 13 14 0 1 2 4 5 6 7 8 9 10 11 12 13 14 0 1 2 3 5 6 7 8 9 10 11 12 13 14 0 1 2 3 4 6 7 8 9 10 11 12 13 14 0 1 2 3 4 5 7 8 9 10 11 12 13 14 0 1 2 3 4 5 6 8 9 10 11 12 13 14 0 1 2 3 4 5 6 7 9 10 11 12 13 14 0 1 2 3 4 5 6 7 8 10 11 12 13 14 0 1 2 3 4 5 6 7 8 9 11 12 13 14 0 1 2 3 4 5 6 7 8 9 10 12 13 14 0 1 2 3 4 5 6 7 8 9 10 11 13 14 0 1 2 3 4 5 6 7 8 9 10 11 12 14 0 1 2 3 4 5 6 7 8 9 10 11 12 13 a(16)>=244744192 Announcement: https://users.monash.edu.au/~iwanless/data/transversals/, Ian Wanless et al. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 2 3 0 1 5 4 7 6 9 8 11 10 14 15 12 13 3 2 1 0 6 7 4 5 10 11 8 9 15 14 13 12 1 0 3 2 7 6 5 4 11 10 9 8 13 12 15 14 8 11 9 10 14 12 13 15 0 2 3 1 5 6 4 7 10 9 11 8 13 15 14 12 3 1 0 2 7 4 6 5 11 8 10 9 15 13 12 14 1 3 2 0 6 5 7 4 9 10 8 11 12 14 15 13 2 0 1 3 4 7 5 6 14 15 12 13 8 9 10 11 4 5 6 7 2 3 0 1 13 12 15 14 10 11 8 9 6 7 4 5 1 0 3 2 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 12 13 14 15 9 8 11 10 5 4 7 6 0 1 2 3 6 5 7 4 3 1 0 2 13 15 14 12 11 8 10 9 7 4 6 5 1 3 2 0 15 13 12 14 10 9 11 8 4 7 5 6 0 2 3 1 14 12 13 15 9 10 8 11 5 6 4 7 2 0 1 3 12 14 15 13 8 11 9 10 n=17, a(17)>=1606008513 Announcement: https://users.monash.edu.au/~iwanless/data/transversals/, Ian Wanless et al. 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)>=6434611200 Announcement: https://users.monash.edu.au/~iwanless/data/transversals/, Ian Wanless et al. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 10 11 12 4 5 6 7 8 9 1 2 3 13 14 15 16 17 0 11 12 4 5 6 7 8 9 10 2 3 13 14 15 16 17 0 1 12 4 5 6 7 8 9 10 11 3 13 14 15 16 17 0 1 2 4 5 6 7 8 9 10 11 12 13 14 15 16 17 0 1 2 3 5 6 7 8 9 10 11 12 4 14 15 16 17 0 1 2 3 13 6 7 8 9 10 11 12 4 5 15 16 17 0 1 2 3 13 14 7 8 9 10 11 12 4 5 6 16 17 0 1 2 3 13 14 15 8 9 10 11 12 4 5 6 7 17 0 1 2 3 13 14 15 16 9 10 11 12 13 14 15 16 17 0 1 2 3 4 5 6 7 8 1 2 3 13 14 15 16 17 0 10 11 12 4 5 6 7 8 9 2 3 13 14 15 16 17 0 1 11 12 4 5 6 7 8 9 10 3 13 14 15 16 17 0 1 2 12 4 5 6 7 8 9 10 11 13 14 15 16 17 0 1 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 0 1 2 3 13 5 6 7 8 9 10 11 12 4 15 16 17 0 1 2 3 13 14 6 7 8 9 10 11 12 4 5 16 17 0 1 2 3 13 14 15 7 8 9 10 11 12 4 5 6 17 0 1 2 3 13 14 15 16 8 9 10 11 12 4 5 6 7 n=19, a(19)>=87656896891 Announcement: https://users.monash.edu.au/~iwanless/data/transversals/, Ian Wanless et al. 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)>=697292390400 Announcement: https://users.monash.edu.au/~iwanless/data/transversals/, Ian Wanless et al. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 2 3 4 0 1 7 8 9 5 6 12 13 14 10 11 17 18 19 15 16 4 0 1 2 3 9 5 6 7 8 14 10 11 12 13 19 15 16 17 18 1 2 3 4 0 6 7 8 9 5 11 12 13 14 10 16 17 18 19 15 3 4 0 1 2 8 9 5 6 7 13 14 10 11 12 18 19 15 16 17 15 16 17 18 19 10 11 12 13 14 5 6 7 8 9 0 1 2 3 4 17 18 19 15 16 12 13 14 10 11 7 8 9 5 6 2 3 4 0 1 19 15 16 17 18 14 10 11 12 13 9 5 6 7 8 4 0 1 2 3 16 17 18 19 15 11 12 13 14 10 6 7 8 9 5 1 2 3 4 0 18 19 15 16 17 13 14 10 11 12 8 9 5 6 7 3 4 0 1 2 5 6 7 8 9 0 1 2 3 4 15 16 17 18 19 10 11 12 13 14 7 8 9 5 6 2 3 4 0 1 17 18 19 15 16 12 13 14 10 11 9 5 6 7 8 4 0 1 2 3 19 15 16 17 18 14 10 11 12 13 6 7 8 9 5 1 2 3 4 0 16 17 18 19 15 11 12 13 14 10 8 9 5 6 7 3 4 0 1 2 18 19 15 16 17 13 14 10 11 12 10 11 12 13 14 15 16 17 18 19 0 1 2 3 4 5 6 7 8 9 12 13 14 10 11 17 18 19 15 16 2 3 4 0 1 7 8 9 5 6 14 10 11 12 13 19 15 16 17 18 4 0 1 2 3 9 5 6 7 8 11 12 13 14 10 16 17 18 19 15 1 2 3 4 0 6 7 8 9 5 13 14 10 11 12 18 19 15 16 17 3 4 0 1 2 8 9 5 6 7 n=21 ? n=22 ? n=23, a(23)>=452794797220965 Announcement: https://oeis.org/A006717, Ian Wanless, Oct 07 2001 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 0 1 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 0 1 2 3 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 0 1 2 3 4 5 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 0 1 2 3 4 5 6 7 10 11 12 13 14 15 16 17 18 19 20 21 22 0 1 2 3 4 5 6 7 8 9 12 13 14 15 16 17 18 19 20 21 22 0 1 2 3 4 5 6 7 8 9 10 11 14 15 16 17 18 19 20 21 22 0 1 2 3 4 5 6 7 8 9 10 11 12 13 16 17 18 19 20 21 22 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 18 19 20 21 22 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 20 21 22 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 22 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 0 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 0 1 2 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 0 1 2 3 4 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 0 1 2 3 4 5 6 9 10 11 12 13 14 15 16 17 18 19 20 21 22 0 1 2 3 4 5 6 7 8 11 12 13 14 15 16 17 18 19 20 21 22 0 1 2 3 4 5 6 7 8 9 10 13 14 15 16 17 18 19 20 21 22 0 1 2 3 4 5 6 7 8 9 10 11 12 15 16 17 18 19 20 21 22 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 17 18 19 20 21 22 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 19 20 21 22 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 21 22 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 n=24 ? n=25, a(25)>=41609568918940625 Announcement: https://oeis.org/A006717, Ian Wanless, Oct 07 2001 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 0 1 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 0 1 2 3 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 0 1 2 3 4 5 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 0 1 2 3 4 5 6 7 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 0 1 2 3 4 5 6 7 8 9 12 13 14 15 16 17 18 19 20 21 22 23 24 0 1 2 3 4 5 6 7 8 9 10 11 14 15 16 17 18 19 20 21 22 23 24 0 1 2 3 4 5 6 7 8 9 10 11 12 13 16 17 18 19 20 21 22 23 24 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 18 19 20 21 22 23 24 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 20 21 22 23 24 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 22 23 24 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 24 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 0 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 0 1 2 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 0 1 2 3 4 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 0 1 2 3 4 5 6 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 0 1 2 3 4 5 6 7 8 11 12 13 14 15 16 17 18 19 20 21 22 23 24 0 1 2 3 4 5 6 7 8 9 10 13 14 15 16 17 18 19 20 21 22 23 24 0 1 2 3 4 5 6 7 8 9 10 11 12 15 16 17 18 19 20 21 22 23 24 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 17 18 19 20 21 22 23 24 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 19 20 21 22 23 24 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 21 22 23 24 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 23 24 0 1 2 3 4 5 6 7 8 9 10 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