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%I #60 Aug 08 2023 22:22:52
%S 1,0,0,1,2,2,972,4873096,3292326155394
%N Number of main classes of diagonal Latin squares of order n.
%H A. D. Belyshev, <a href="https://vk.com/wall162891802_881">Discussion about properties of diagonal Latin squares</a> (in Russian)
%H 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 E. I. Vatutin, A. D. Belyshev, <a href="http://forum.boinc.ru/default.aspx?g=posts&m=87549#post87549">Discussion about properties of diagonal Latin squares at forum.boinc.ru</a> (in Russian)
%H E. I. Vatutin, <a href="https://vk.com/wall162891802_1315">Enumerating the diagonal Latin squares of order 8 using equivalence classes of X-based fillings of diagonals and ESODLS-schemas</a> (in Russian)
%H E. I. Vatutin, <a href="https://vk.com/wall162891802_1330">Enumerating the diagonal Latin squares of order 9 using Gerasim@Home volunteer distributed computing project, equivalence classes of X-based fillings of diagonals and ESODLS-schemas</a> (in Russian)
%H E. Vatutin, A. Belyshev, S. Kochemazov, O. Zaikin, N. Nikitina, <a href="http://evatutin.narod.ru/evatutin_co_dls_cfs_cnt.pdf">Enumeration of isotopy classes of diagonal Latin squares of small order using volunteer computing</a>, Supercomputing Days Russia 2018, Moscow, Moscow State University, 2018, pp. 933-942.
%H Eduard Vatutin, Alexey Belyshev, Stepan Kochemazov, Oleg Zaikin, Natalia Nikitina, <a href="http://russianscdays.org/files/pdf18/933.pdf">Enumeration of Isotopy Classes of Diagonal Latin Squares of Small Order Using Volunteer Computing</a>, Russian Supercomputing Days (Суперкомпьютерные дни в России), 2018.
%H E. Vatutin, A. Belyshev, S. Kochemazov, O. Zaikin, N. Nikitina, <a href="https://doi.org/10.1007/978-3-030-05807-4_49">Enumeration of isotopy classes of diagonal Latin squares of small order using volunteer computing</a>, Communications in Computer and Information Science. Vol. 965. Springer, 2018. pp. 578-586.
%H E. I. Vatutin, A. D. Belyshev, N. N. Nikitina, and M. O. Manzuk, <a href="http://evatutin.narod.ru/evatutin_dls_scf_gen.pdf">Use of X-based diagonal fillings and ESODLS CMS schemes for enumeration of main classes of diagonal Latin squares</a>, Telecommunications, 2023, No. 1, pp. 2-16, DOI: 10.31044/1684-2588-2023-0-1-2-16 (in Russian).
%H Eduard I. Vatutin, Natalia N. Nikitina, 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. Third independent confirmation of the previously calculated value a(9)</a> (in Russian).
%H E. I. Vatutin, N. N. Nikitina, M. O. Manzuk, A. M. Albertyan and I. I. Kurochkin, <a href="http://evatutin.narod.ru/evatutin_spectra_t_dt_i_o_small_orders_thesis.pdf">On the construction of spectra of fast-computable numerical characteristics for diagonal Latin squares of small order</a>, Intellectual and Information Systems (Intellect - 2021). Tula, 2021. pp. 7-17. (in Russian)
%H <a href="/index/La#Latin">Index entries for sequences related to Latin squares and rectangles</a>
%Y Cf. A003090, A309283, A274171.
%K nonn,hard,more
%O 1,5
%A _Eduard I. Vatutin_, May 31 2017
%E a(9) from _Eduard I. Vatutin_, Jul 06 2019
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