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A366332
Minimum number of diagonal transversals in a semicyclic diagonal Latin square of order 2n+1.
2
1, 0, 5, 27, 0, 4523, 127339, 0, 204330233, 11232045257, 0
OFFSET
0,3
COMMENTS
A horizontally semicyclic diagonal Latin square is a square where each row r(i) is a cyclic shift of the first row r(0) by some value d(i) (see example). Similarly, a vertically semicyclic diagonal Latin square is a square where each column c(i) is a cyclic shift of the first column c(0) by some value d(i).
EXAMPLE
Example of horizontally semicyclic diagonal Latin square of order 13:
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 (d=2)
4 5 6 7 8 9 10 11 12 0 1 2 3 (d=4)
9 10 11 12 0 1 2 3 4 5 6 7 8 (d=9)
7 8 9 10 11 12 0 1 2 3 4 5 6 (d=7)
12 0 1 2 3 4 5 6 7 8 9 10 11 (d=12)
3 4 5 6 7 8 9 10 11 12 0 1 2 (d=3)
11 12 0 1 2 3 4 5 6 7 8 9 10 (d=11)
6 7 8 9 10 11 12 0 1 2 3 4 5 (d=6)
1 2 3 4 5 6 7 8 9 10 11 12 0 (d=1)
5 6 7 8 9 10 11 12 0 1 2 3 4 (d=5)
10 11 12 0 1 2 3 4 5 6 7 8 9 (d=10)
8 9 10 11 12 0 1 2 3 4 5 6 7 (d=8)
CROSSREFS
KEYWORD
nonn,more,hard
AUTHOR
Eduard I. Vatutin, Oct 07 2023
STATUS
approved