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%I #25 Mar 04 2023 02:31:20
%S 1,0,0,8,15,0,23,16,132
%N Minimum number of transversals in an orthogonal diagonal Latin square of order n.
%C Orthogonal diagonal Latin squares is a diagonal Latin squares that have at least one orthogonal diagonal mate.
%C a(10) <= 668, a(11) <= 2091, a(12) <= 6240.
%C Every diagonal Latin square is a Latin square and every orthogonal diagonal Latin square is a diagonal Latin square, so 0 <= A287645(n) <= a(n) <= A287644(n) <= A090741(n). - _Eduard I. Vatutin_, Feb 17 2023
%H Eduard I. Vatutin, <a href="https://vk.com/wall162891802_1709">About the spectra of numerical characteristics of orthogonal diagonal Latin squares of orders 1-11</a> (in Russian).
%H Eduard I. Vatutin, <a href="/A357514/a357514.txt">Proving list (best known examples)</a>
%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. A287644, A287645, A344105, A350585.
%K nonn,more,hard
%O 1,4
%A _Eduard I. Vatutin_, Oct 01 2022
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