cp's OEIS Frontend

A333366 Number of main classes of doubly self-orthogonal diagonal Latin squares of order n.

%I A333366 #46 Sep 09 2023 18:00:24
%S A333366 1,0,0,1,1,0,2,8,88,0
%N A333366 Number of main classes of doubly self-orthogonal diagonal Latin squares of order n.
%C A333366 A doubly self-orthogonal diagonal Latin square (DSODLS) is a diagonal Latin square orthogonal to its transpose and antitranspose.
%C A333366 a(n) <= A329685(n) <= A309210(n) <= A330391(n). - _Eduard I. Vatutin_, Jun 01 2020
%H A333366 R. Lu, S. Liu, and J. Zhang, <a href="https://doi.org/10.1007/978-3-642-23786-7_41">Searching for Doubly Self-orthogonal Latin Squares</a>. Lecture Notes in Computer Science 6876 (2011), 538-545.
%H A333366 E. I. Vatutin, <a href="https://vk.com/wall162891802_1105">About the number of DSODLS of orders 1-10</a> (in Russian).
%H A333366 E. I. Vatutin, <a href="http://evatutin.narod.ru/evatutin_dsodls_1_to_10.zip">List of all main classes of doubly self-orthogonal diagonal Latin squares of orders 1-10</a>.
%H A333366 E. I. Vatutin, <a href="http://evatutin.narod.ru/evatutin_dls_spec_types_list.pdf">Special types of diagonal Latin squares</a>, Cloud and distributed computing systems in electronic control conference, within the National supercomputing forum (NSCF - 2022). Pereslavl-Zalessky, 2023. pp. 9-18. (in Russian)
%H A333366 E. I. Vatutin and A. D. Belyshev, <a href="http://evatutin.narod.ru/evatutin_sodls_and_dsodls_1_to_10.pdf">About the number of self-orthogonal (SODLS) and doubly self-orthogonal diagonal Latin squares (DSODLS) of orders 1-10</a>. High-performance computing systems and technologies. Vol. 4. No. 1. 2020. pp. 58-63. (in Russian)
%H A333366 E. Vatutin and A. Belyshev, <a href="https://www.springerprofessional.de/en/enumerating-the-orthogonal-diagonal-latin-squares-of-small-order/18659992">Enumerating the Orthogonal Diagonal Latin Squares of Small Order for Different Types of Orthogonality</a>, Communications in Computer and Information Science, Vol. 1331, Springer, 2020, pp. 586-597.
%H A333366 Eduard I. Vatutin, Natalia N. Nikitina, and Maxim O. Manzuk, <a href="https://vk.com/wall162891802_1485">First results of an experiment on studying the properties of DLS of order 9 in the volunteer distributed computing projects Gerasim@Home and RakeSearch</a> (in Russian).
%H A333366 <a href="/index/La#Latin">Index entries for sequences related to Latin squares and rectangles</a>.
%e A333366 0 1 2 3 4 5 6 7 8
%e A333366 2 4 3 0 7 6 8 1 5
%e A333366 4 6 7 1 8 2 3 5 0
%e A333366 8 3 5 6 0 7 1 2 4
%e A333366 7 8 1 4 5 3 0 6 2
%e A333366 3 7 0 2 1 8 5 4 6
%e A333366 1 5 4 7 6 0 2 8 3
%e A333366 5 0 6 8 2 1 4 3 7
%e A333366 6 2 8 5 3 4 7 0 1
%Y A333366 Cf. A329685, A309210, A333367.
%K A333366 nonn,more,hard
%O A333366 1,7
%A A333366 _Eduard I. Vatutin_, Mar 17 2020
%E A333366 a(10) = 0 is established by Lu et al. (2011).