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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A369379 Number of Dabbaghian-Wu pandiagonal Latin squares of order 2n+1 with the first row in order.

Original entry on oeis.org

1, 0, 0, 4, 0, 0, 72, 0, 0, 108, 0, 0, 4, 0, 0, 180, 0, 3, 216, 0, 0, 252, 0, 0, 264, 0, 0, 0, 0, 0, 360, 0, 5, 396, 0, 0, 432, 0, 0, 468, 0, 0, 0, 0, 0, 868, 0, 5, 576, 0
Offset: 1

Views

Author

Eduard I. Vatutin, Jan 22 2024

Keywords

Comments

A pandiagonal Latin square is a Latin square in which the diagonal, antidiagonal and all broken diagonals and antidiagonals are transversals.
A Dabbaghian-Wu pandiagonal Latin square (see A368027) is a special type of pandiagonal Latin square (see A342306). Such squares are constructed from cyclic diagonal Latin squares (see A338562) for prime orders n=6k+1 (see Dabbaghian and Wu article) using a polynomial algorithm based on permutation of some values in Latin square. For other orders (25, 35, 49, ...) this algorithm also ensures correct pandiagonal Latin squares.

Examples

			n=13=6*2+1 (prime order):
.
 0  1  2  3  4  5  6  7  8  9 10 11 12
 2  3  0  1 11 12  8  4 10  7  5  6  9
 4 10 11  2  8  1  3  0 12  6  9  7  5
11  5  9  7 10  0 12  1  3  2  8  4  6
 8  7 10  5  9  6 11  2  0  4  3 12  1
12  0  4  6  7  2  9 10  5 11  1  8  3
 1  6 12  8  3  4  5 11  9 10  7  2  0
 9  2  3  4 12  8  1  6  7  5  0 10 11
10 11  5  0  1  3  7  8  4 12  6  9  2
 5  9  1 11  2 10  0 12  6  8  4  3  7
 6  8  7 10  0 11  2  9  1  3 12  5  4
 7  4  6 12  5  9 10  3  2  0 11  1  8
 3 12  8  9  6  7  4  5 11  1  2  0 10
.
n=19=6*3+1 (prime order):
.
 0  1  2  3  4  5  6  7  8  9 10 11 12
 2  3  0  1 11 12  8  4 10  7  5  6  9
 4 10 11  2  8  1  3  0 12  6  9  7  5
11  5  9  7 10  0 12  1  3  2  8  4  6
 8  7 10  5  9  6 11  2  0  4  3 12  1
12  0  4  6  7  2  9 10  5 11  1  8  3
 1  6 12  8  3  4  5 11  9 10  7  2  0
 9  2  3  4 12  8  1  6  7  5  0 10 11
10 11  5  0  1  3  7  8  4 12  6  9  2
 5  9  1 11  2 10  0 12  6  8  4  3  7
 6  8  7 10  0 11  2  9  1  3 12  5  4
 7  4  6 12  5  9 10  3  2  0 11  1  8
 3 12  8  9  6  7  4  5 11  1  2  0 10
.
n=25=6*4+1 (nonprime order):
.
 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
 3  4 15  6  7  8  9  5 11 12 13 14  0 16 17 18 19 10 21 22 23 24 20  1  2
 6  7  8  9 10 11 12 13 14 15 16 17 18 19  0 21 22 23 24  5  1  2  3  4 20
 9  5 11 12 13 14 10 16 17 18 19 20 21 22 23 24  0  1  2  3  4 15  6  7  8
12 13 14  0 16 17 18 19 10 21 22 23 24  5  1  2  3  4 20  6  7  8  9 15 11
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
18 19 10 21 22 23 24 20  1  2  3  4 15  6  7  8  9  5 11 12 13 14  0 16 17
21 22 23 24  5  1  2  3  4 20  6  7  8  9 10 11 12 13 14 15 16 17 18 19  0
24  0  1  2  3  4 15  6  7  8  9  5 11 12 13 14 10 16 17 18 19 20 21 22 23
 2  3  4 20  6  7  8  9 15 11 12 13 14  0 16 17 18 19 10 21 22 23 24  5  1
 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
 8  9  5 11 12 13 14  0 16 17 18 19 10 21 22 23 24 20  1  2  3  4 15  6  7
11 12 13 14 15 16 17 18 19  0 21 22 23 24  5  1  2  3  4 20  6  7  8  9 10
14 10 16 17 18 19 20 21 22 23 24  0  1  2  3  4 15  6  7  8  9  5 11 12 13
17 18 19 10 21 22 23 24  5  1  2  3  4 20  6  7  8  9 15 11 12 13 14  0 16
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
23 24 20  1  2  3  4 15  6  7  8  9  5 11 12 13 14  0 16 17 18 19 10 21 22
 1  2  3  4 20  6  7  8  9 10 11 12 13 14 15 16 17 18 19  0 21 22 23 24  5
 4 15  6  7  8  9  5 11 12 13 14 10 16 17 18 19 20 21 22 23 24  0  1  2  3
 7  8  9 15 11 12 13 14  0 16 17 18 19 10 21 22 23 24  5  1  2  3  4 20  6
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
13 14  0 16 17 18 19 10 21 22 23 24 20  1  2  3  4 15  6  7  8  9  5 11 12
16 17 18 19  0 21 22 23 24  5  1  2  3  4 20  6  7  8  9 10 11 12 13 14 15
19 20 21 22 23 24  0  1  2  3  4 15  6  7  8  9  5 11 12 13 14 10 16 17 18
22 23 24  5  1  2  3  4 20  6  7  8  9 15 11 12 13 14  0 16 17 18 19 10 21

Links

Crossrefs

Cf. A338562, A342306, A368027, A369380.

A369380 Number of main classes of diagonal Latin squares containing Dabbaghian-Wu pandiagonal Latin squares of order 2n+1.

Original entry on oeis.org

1, 0, 0, 1, 0, 0, 8, 0, 0, 18, 0, 0
Offset: 1

Views

Author

Eduard I. Vatutin, Jan 22 2024

Keywords

Comments

A pandiagonal Latin square is a Latin square in which the diagonal, antidiagonal and all broken diagonals and antidiagonals are transversals.
A Dabbaghian-Wu pandiagonal Latin square (see A368027) is a special type of pandiagonal Latin square (see A342306). Such squares are constructed from cyclic diagonal Latin squares (see A338562) for prime orders n=6k+1 (see Dabbaghian and Wu article) using a polynomial algorithm based on permutation of some values in Latin square. For other orders (25, 35, 49, ...) this algorithm also ensures correct pandiagonal Latin squares.

Links

Crossrefs

Cf. A338562, A342306, A368027, A369379.
Showing 1-2 of 2 results.

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