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A360220 Maximum number of diagonal transversals in an orthogonal diagonal Latin square of order n.

%I A360220 #26 Mar 24 2023 18:21:19
%S A360220 1,0,0,4,5,0,27,120,333
%N A360220 Maximum number of diagonal transversals in an orthogonal diagonal Latin square of order n.
%C A360220 An orthogonal diagonal Latin square is a diagonal Latin square that has at least one orthogonal diagonal mate.
%C A360220 a(10) >= 866, a(11) >= 4828, a(12) >= 30192, a(13) >= 131106, a(17) >= 204995269, a(19) >= 11254190082.
%C A360220 For most orders n, at least one diagonal Latin square with the maximal number of diagonal transversals has an orthogonal mate and A287648(n) = a(n). Known exceptions: n=6 and n=10. - _Eduard I. Vatutin_, Feb 17 2023
%C A360220 Every orthogonal diagonal Latin square is a diagonal Latin square, so A287647(n) <= A354068(n) <= a(n) <= A287648(n). - _Eduard I. Vatutin_, Mar 04 2023
%H A360220 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 A360220 Eduard I. Vatutin, <a href="/A360220/a360220.txt">Proving list (best known examples)</a>.
%H A360220 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 A360220 <a href="/index/La#Latin">Index entries for sequences related to Latin squares and rectangles</a>.
%Y A360220 Cf. A287647, A287648, A305570, A305571, A349199, A354068.
%K A360220 nonn,more,hard
%O A360220 1,4
%A A360220 _Eduard I. Vatutin_, Jan 30 2023