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A342997
Maximum number of diagonal transversals in a cyclic diagonal Latin square of order 2n+1.
5
1, 0, 5, 27, 0, 4665, 131106, 0, 204995269, 11254190082
OFFSET
0,3
COMMENTS
A cyclic Latin square is a Latin square in which row i is obtained by cyclically shifting row i-1 by d places (see A338562, A123565 and A341585).
Cyclic diagonal Latin squares do not exist for even n.
All cyclic diagonal Latin squares are diagonal Latin squares, so a((n-1)/2) <= A287648(n).
All diagonal transversals are transversals, so a(n) <= A006717(n).
A342998 <= a(n).
EXAMPLE
For n=2 one of the best cyclic diagonal Latin squares of order 5
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
has a(2)=5 diagonal transversals:
0 . . . . . 1 . . . . . 2 . . . . . 3 . . . . . 4
. . 4 . . . . . 0 . . . . . 1 2 . . . . . 3 . . .
. . . . 3 4 . . . . . 0 . . . . . 1 . . . . . 2 .
. 2 . . . . . 3 . . . . . 4 . . . . . 0 1 . . . .
. . . 1 . . . . . 2 3 . . . . . 4 . . . . . 0 . .
CROSSREFS
KEYWORD
nonn,more,hard
AUTHOR
Eduard I. Vatutin, Apr 02 2021
STATUS
approved