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

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

Offset

0,6

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).

Links

Table of n, a(n) for n=0..13.

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.

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

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

Sequence in context: A073444 A301637 A366333 * A210416 A351312 A220943

Adjacent sequences: A366328 A366329 A366330 * A366332 A366333 A366334

Keyword

nonn,more,hard

Author

Eduard I. Vatutin, Oct 07 2023

Extensions

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

Status

approved