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%I A329685 #75 Aug 08 2023 22:22:15
%S A329685 1,0,0,1,1,0,2,8,470,30502
%N A329685 Number of main classes of self-orthogonal diagonal Latin squares of order n.
%C A329685 A self-orthogonal diagonal Latin square is a diagonal Latin square orthogonal to its transpose.
%C A329685 A333366(n) <= a(n) <= A309210(n) <= A330391(n). - _Eduard I. Vatutin_, Apr 26 2020
%H A329685 A. D. Belyshev, <a href="/A329685/a329685.txt">List of 30502 essentially distinct self-orthogonal diagonal Latin squares of order 10</a>
%H A329685 E. I. Vatutin, <a href="https://vk.com/wall162891802_1085">Discussion about properties of diagonal Latin squares</a> (in Russian).
%H A329685 E. I. Vatutin, <a href="https://vk.com/wall162891802_1086">About the number of main classes for SODLS of order 9</a> (in Russian).
%H A329685 E. I. Vatutin, <a href="https://vk.com/wall162891802_1136">About the number of SODLS of order 10</a> (in Russian).
%H A329685 E. I. Vatutin, <a href="http://evatutin.narod.ru/evatutin_sodls_1_to_10.zip">List of all main classes of self-orthogonal diagonal Latin squares of orders 1-10</a>.
%H A329685 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 A329685 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 A329685 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 A329685 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 A329685 <a href="/index/La#Latin">Index entries for sequences related to Latin squares and rectangles</a>
%e A329685 0 1 2 3 4 5 6 7 8 9
%e A329685 5 2 0 9 7 8 1 4 6 3
%e A329685 9 5 7 1 8 6 4 3 0 2
%e A329685 7 8 6 4 9 2 5 1 3 0
%e A329685 8 9 5 0 3 4 2 6 7 1
%e A329685 3 6 9 5 2 1 7 0 4 8
%e A329685 4 3 1 7 6 0 8 2 9 5
%e A329685 6 7 8 2 5 3 0 9 1 4
%e A329685 2 0 4 6 1 9 3 8 5 7
%e A329685 1 4 3 8 0 7 9 5 2 6
%Y A329685 Cf. A309210, A287761, A287762.
%K A329685 nonn,more,hard
%O A329685 1,7
%A A329685 _Eduard I. Vatutin_, Feb 25 2020
%E A329685 a(9) from _Eduard I. Vatutin_, Mar 12 2020
%E A329685 a(10) from _Eduard I. Vatutin_, Mar 14 2020
%E A329685 a(10) corrected by _Natalia Makarova_, Apr 10 2020

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