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
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)
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
KEYWORD
nonn,more,hard
AUTHOR
Eduard I. Vatutin, Jun 26 2021
STATUS
approved