A345761 a(n) is the number of distinct numbers of orthogonal diagonal mates that a diagonal Latin squares of order n can have.

1, 0, 0, 1, 2, 1, 3, 31, 99

Offset

1,5

Comments

a(n) <= A287695(n) + 1.

a(n) <= A287764(n).

a(10) >= 10. It seems that a(10) = 10 due to long computational experiments within the Gerasim@Home volunteer distributed computing project did not reveal the existence of diagonal Latin squares of order 10 with the number of orthogonal diagonal Latin squares different from {0, 1, 2, 3, 4, 5, 6, 7, 8, 10}.

a(11) >= 112, a(12) >= 5079. - Eduard I. Vatutin, Nov 02 2021, updated Jan 23 2023

Links

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

Eduard I. Vatutin, About the spectra of numerical characteristics of diagonal Latin squares of orders 1-7 (in Russian).

Eduard I. Vatutin, About the spectra of numerical characteristics of diagonal Latin squares of order 8 (in Russian).

Eduard I. Vatutin, About the spectrum of orthogonal diagonal Latin squares for one diagonal Latin squares of order 9 (in Russian).

Eduard I. Vatutin, About the lower bound for a spectrum of orthogonal diagonal Latin squares for one diagonal Latin squares of order 10 (in Russian).

Eduard I. Vatutin, About the lower bound for a spectrum of orthogonal diagonal Latin squares for one diagonal Latin squares of order 11 (in Russian).

Eduard I. Vatutin, Graphical representation of the spectra.

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)

E. I. Vatutin, V. S. Titov, A. I. Pykhtin, A. V. Kripachev, N. N. Nikitina, M. O. Manzuk, A. M. Albertyan and I. I. Kurochkin, Estimation of the Cardinalities of the Spectra of Fast-computable Numerical Characteristics for Diagonal Latin Squares of Orders N>9 (in Russian) // Science and education in the development of industrial, social and economic spheres of Russian regions. Murom, 2022. pp. 314-315.

E. I. Vatutin, V. S. Titov, A. I. Pykhtin, A. V. Kripachev, N. N. Nikitina, M. O. Manzuk, A. M. Albertyan, I. I. Kurochkin, Heuristic method for getting approximations of spectra of numerical characteristics for diagonal Latin squares, Intellectual information systems: trends, problems, prospects, Kursk, 2022. pp. 35-41. (in Russian)

Eduard I. Vatutin, Proving lists (1, 4, 5, 6, 7, 8, 9, 10, 11, 12).

Index entries for sequences related to Latin squares and rectangles.

Example

For n=7 the number of orthogonal diagonal Latin squares that a diagonal Latin square of order 7 may have is 0, 1, or 3. Since there are 3 distinct values, a(7)=3.

Crossrefs

Cf. A287695, A287764, A309344, A344105, A345370, A345760.

Sequence in context: A337891 A354196 A059333 * A106485 A126008 A096098

Adjacent sequences: A345758 A345759 A345760 * A345762 A345763 A345764

Keyword

nonn,more,hard

Author

Eduard I. Vatutin, Jun 26 2021

Status

approved