A338562 -id:A338562 - cp's OEIS frontend

A375475 Number of main classes of diagonalized cyclic diagonal Latin squares of order 2n+1.

1, 0, 1, 1, 7, 81, 2933

Offset: 0

Eduard I. Vatutin, Aug 17 2024

Diagonalized cyclic diagonal Latin squares are diagonal Latin squares that are isomorphic to cyclic Latin squares. They are can be obtained from cyclic Latin squares (see A338522) by diagonalization (getting a corresponding pair of transversals and placing them on the diagonals, see article). Diagonalized cyclic diagonal Latin squares have some interesting properties, for example, there are a large number of diagonal transversals for diagonal Latin squares of odd orders.

Eduard I. Vatutin, Special types of diagonal Latin squares, Cloud and distributed computing systems in electronic control conference, within the National supercomputing forum (NSCF - 2022). Pereslavl-Zalessky, 2023. pp. 9-18. (in Russian)
Eduard I. Vatutin, About the different types of cyclic diagonal Latin squares (in Russian).
E. Vatutin, A. Belyshev, N. Nikitina, M. Manzuk, A. Albertian, I. Kurochkin, A. Kripachev, and A. Pykhtin, Diagonalization and Canonization of Latin Squares, Lecture Notes in Computer Science, Vol. 14389, Springer, Cham., 2023. pp. 48-61.
Proving lists.
Index entries for sequences related to Latin squares and rectangles.

Cf. A338522, A338562, A372922, A372923.

A343866 Number of inequivalent cyclic diagonal Latin squares of order 2n+1 up to rotations, reflections and permutation of symbols.

Original entry on oeis.org

1, 0, 1, 1, 0, 2, 3, 0, 4, 4, 0, 5, 3, 0, 7, 7, 0, 2, 9, 0, 10, 10, 0, 11, 7, 0, 13, 4, 0, 14, 15, 0, 6, 16, 0, 17, 18, 0, 8, 19, 0, 20, 8, 0, 22, 10, 0, 8, 24, 0, 25, 25, 0, 26, 27, 0, 28, 10, 0, 14, 22, 0, 13, 31, 0, 32, 16, 0, 34, 34, 0, 20, 14, 0, 37, 37, 0, 14, 39, 0, 20

Offset: 0

Andrew Howroyd, May 02 2021

nonn

Also the number of main classes of diagonal Latin squares of order 2n+1 that contain a cyclic Latin square. Compare A341585.

			a(12) = 3 since there are A123565(25) = 10 cyclic diagonal Latin squares whose first row is in ascending order. Each of these is uniquely defined by the step between rows and form 5 pairs by horizontal or vertical reflection (negating the step between rows). Up to exchanging rows with columns there are 3 distinct classes, so a(12) = 3.

Cf. A123565, A287764, A338562, A341585.

iscanon(n,k,g) = k <= vecmin(g*k%n) && k <= vecmin(g*lift(1/Mod(k,n))%n)
a(n)={if(n==0, 1, my(m=2*n+1); sum(k=1, m-1, gcd(m,k)==1 && gcd(m,k-1)==1 && gcd(m,k+1)==1 && iscanon(m, k, [1,-1])))}

a((p-1)/2) = A341585((p-1)/2) for odd prime p.

A366331 Number of main classes of diagonal Latin squares of order 2n+1 that contain a horizontally semicyclic Latin square.

Original entry on oeis.org

1, 0, 1, 1, 0, 2, 20, 0, 272, 1208, 0, 127334, 1958084, 0

Offset: 0

Eduard I. Vatutin, Oct 07 2023

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).

			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)

Eduard I. Vatutin, About the horizontally and vertically semicyclic diagonal Latin squares enumeration (in Russian).
Eduard I. Vatutin, About the spectra of numerical characteristics of different types of cyclic diagonal Latin squares (in Russian).
Eduard I. Vatutin, About the number of main classes of semicyclic diagonal Latin squares of order 17 (in Russian).
Eduard I. Vatutin, About the number of main classes of semicyclic diagonal Latin squares of order 19 (in Russian).
Eduard I. Vatutin, Lists of canonical forms of semicyclic diagonal Latin squares of orders 5-19.
Index entries for sequences related to Latin squares and rectangles.

Cf. A071607, A123565, A287764, A338562, A342990, A343866.

a(11)-a(13) from Andrew Howroyd, Nov 02 2023

A368027 Number of Dabbaghian-Wu pandiagonal Latin squares of order 2n+1.

Original entry on oeis.org

1, 0, 0, 24, 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

Eduard I. Vatutin, Dec 16 2023

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 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.

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

Vahid Dabbaghian and Tiankuang Wu, Constructing non-cyclic pandiagonal Latin squares of prime orders, Journal of Discrete Algorithms, Vol. 30, 2015, pp. 70-77, doi: 10.1016/j.jda.2014.12.001.
Eduard I. Vatutin, About the Dabbaghian-Wu pandiagonal Latin squares for non-prime orders (in Russian).
Index entries for sequences related to Latin squares and rectangles.

Cf. A338562, A369379, A369380, A342306.

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

Eduard I. Vatutin, Jan 22 2024

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.

			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

Vahid Dabbaghian and Tiankuang Wu, Constructing non-cyclic pandiagonal Latin squares of prime orders, Journal of Discrete Algorithms, Vol. 30, 2015, pp. 70-77, doi: 10.1016/j.jda.2014.12.001.
Index entries for sequences related to Latin squares and rectangles.

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

Eduard I. Vatutin, Jan 22 2024

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.

Vahid Dabbaghian and Tiankuang Wu, Constructing non-cyclic pandiagonal Latin squares of prime orders, Journal of Discrete Algorithms, Vol. 30, 2015, pp. 70-77, doi: 10.1016/j.jda.2014.12.001.
Index entries for sequences related to Latin squares and rectangles.

Cf. A338562, A342306, A368027, A369379.

A370672 Number of ways of arranging 2n+1 nonattacking queens on a 2n+1 X 2n+1 toroidal board using knight moves.

Original entry on oeis.org

1, 0, 10, 28, 0, 88, 130, 0, 238, 304, 0, 460, 250, 0, 754, 868, 0, 280, 1258, 0, 1558, 1720, 0, 2068, 1372, 0, 2650, 880, 0, 3304, 3538, 0, 1300, 4288, 0, 4828, 5110, 0, 2464, 6004, 0, 6640, 2380, 0, 7654, 3640, 0

Offset: 0

Eduard I. Vatutin, Feb 25 2024

nonn

All solutions of this type can be found using a knight moving with some displacements dx and dy starting from some cell with coordinates (x,y): (x,y) -> (x+dx,y+dy) -> (x+2*dx,y+2*dy) -> ... -> (x,y) (all operations modulo n). For n <= 11 all solutions of n nonattacking queens on n X n a toroidal board problem are solutions of this type, for n >= 13 some solutions are not of this type (see A051906 for examples).

			For n=2*2+1=5 there are 10 solutions:
.
+-----------+ +-----------+ +-----------+ +-----------+ +-----------+
| Q . . . . | | Q . . . . | | . Q . . . | | . Q . . . | | . . Q . . |
| . . Q . . | | . . . Q . | | . . . Q . | | . . . . Q | | Q . . . . |
| . . . . Q | | . Q . . . | | Q . . . . | | . . Q . . | | . . . Q . |
| . Q . . . | | . . . . Q | | . . Q . . | | Q . . . . | | . Q . . . |
| . . . Q . | | . . Q . . | | . . . . Q | | . . . Q . | | . . . . Q |
+-----------+ +-----------+ +-----------+ +-----------+ +-----------+
.
+-----------+ +-----------+ +-----------+ +-----------+ +-----------+
| . . Q . . | | . . . Q . | | . . . Q . | | . . . . Q | | . . . . Q |
| . . . . Q | | Q . . . . | | . Q . . . | | . Q . . . | | . . Q . . |
| . Q . . . | | . . Q . . | | . . . . Q | | . . . Q . | | Q . . . . |
| . . . Q . | | . . . . Q | | . . Q . . | | Q . . . . | | . . . Q . |
| Q . . . . | | . Q . . . | | Q . . . . | | . . Q . . | | . Q . . . |
+-----------+ +-----------+ +-----------+ +-----------+ +-----------+
.
so a(2)=10.

Eduard I. Vatutin, Arranging of N queens on toroidal board and generating pandiagonal Latin squares using them (in Russian).
Eduard I. Vatutin, Numerical formula between number of cyclic diagonal Latin squares and number of toroidal n-queens problem solutions getting by knight movement (in Russian).
Index entries for sequences related to Latin squares and rectangles.

Cf. A007705, A051906, A123565, A338562.

a(n) = A123565(2*n+1) * (2*n+1).

a(n) = A338562(n) / (2n)!. - Eduard I. Vatutin, Mar 13 2024

A366333 a(n) is the number of distinct numbers of diagonal transversals that a semicyclic diagonal Latin square of order 2n+1 can have.

Original entry on oeis.org

1, 0, 1, 1, 0, 2, 20, 0, 271, 1208, 0

Offset: 0

Eduard I. Vatutin, Oct 07 2023

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). 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). Cyclic diagonal Latin squares (see A338562) fall under the definition of vertically and horizontally semicyclic diagonal Latin squares simultaneously, in this type of squares each row r(i) is obtained from the previous one r(i-1) using cyclic shift by some value d.

Semicyclic diagonal Latin squares do not exist for even orders n.

			For n=6*2+1=13 the number of diagonal transversals that a semicyclic diagonal Latin square of order 13 may have is 127339, 127830, 128489, 128519, 128533, 128608, 128751, 128818, 128861, 129046, 129059, 129171, 129243, 129286, 129353, 129474, 129641, 129657, 130323 or 131106. Since there are 20 distinct values, a(6)=20.

Eduard I. Vatutin, About the spectra of numerical characteristics of different types of cyclic diagonal Latin squares (in Russian).
Eduard I. Vatutin, About the spectra of numerical characteristics of semicyclic diagonal Latin squares of order 17 (in Russian).
Eduard I. Vatutin, About the spectra of numerical characteristics of semicyclic diagonal Latin squares of order 19 (in Russian).
Eduard I. Vatutin, Proving lists (1, 5, 7, 11, 13, 17, 19).
Eduard I. Vatutin, Graphical representation of the spectra.
Index entries for sequences related to Latin squares and rectangles.

Cf. A071607, A341585, A342990, A345370, A366331.

cp's OEIS Frontend

A375475 Number of main classes of diagonalized cyclic diagonal Latin squares of order 2n+1.

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A343866 Number of inequivalent cyclic diagonal Latin squares of order 2n+1 up to rotations, reflections and permutation of symbols.

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A366331 Number of main classes of diagonal Latin squares of order 2n+1 that contain a horizontally semicyclic Latin square.

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A368027 Number of Dabbaghian-Wu pandiagonal Latin squares of order 2n+1.

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

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

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A370672 Number of ways of arranging 2n+1 nonattacking queens on a 2n+1 X 2n+1 toroidal board using knight moves.

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A366333 a(n) is the number of distinct numbers of diagonal transversals that a semicyclic diagonal Latin square of order 2n+1 can have.

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