A349199 a(n) is the number of distinct numbers of diagonal transversals that an orthogonal diagonal Latin square of order n can have.

1, 0, 0, 1, 1, 0, 3, 31, 165

Offset

1,7

Comments

An orthogonal diagonal Latin square is a diagonal Latin square with at least one orthogonal diagonal mate. Since all orthogonal diagonal Latin squares are diagonal Latin squares, a(n) <= A345370(n).

a(10) >= 390, a(11) >= 560, a(12) >= 13429. - Eduard I. Vatutin, Nov 10 2021, updated Jan 29 2023

Links

Table of n, a(n) for n=1..9.

Eduard I. Vatutin, About the spectra of numerical characteristics of orthogonal diagonal Latin squares of orders 1-11 (in Russian).

Eduard I. Vatutin, Graphical representation of the spectra.

Eduard I. Vatutin, Proving lists (1, 4, 5, 7, 8, 9, 10, 11, 12).

E. I. Vatutin, N. N. Nikitina, M. O. Manzuk, A. M. Albertyan and I. I. Kurochkin, On the construction of spectra of fast-computable numerical characteristics for diagonal Latin squares of small order, Intellectual and Information Systems (Intellect - 2021). Tula, 2021. pp. 7-17. (in Russian)

Index entries for sequences related to Latin squares and rectangles.

Example

For n=8 the number of diagonal transversals that an orthogonal diagonal Latin square of order 8 may have is 8, 9, 10, 12, 14, 15, 16, 17, 18, 20, 22, 23, 24, 25, 26, 28, 30, 32, 36, 38, 40, 42, 44, 48, 52, 56, 64, 72, 88, 96, or 120. Since there are 31 distinct values, a(8)=31.

Crossrefs

Cf. A305570, A345370.

Sequence in context: A089286 A089287 A125085 * A007233 A197892 A198009

Adjacent sequences: A349196 A349197 A349198 * A349200 A349201 A349202

Keyword

nonn,more,hard

Author

Eduard I. Vatutin, Nov 10 2021

Status

approved