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A354068 Minimum number of diagonal transversals in an orthogonal diagonal Latin square of order n.

%I A354068 #16 Mar 20 2023 21:06:19
%S A354068 1,0,0,4,5,0,8,8,14
%N A354068 Minimum number of diagonal transversals in an orthogonal diagonal Latin square of order n.
%C A354068 An orthogonal diagonal Latin square is a diagonal Latin square with at least one orthogonal diagonal mate.
%C A354068 a(10) <= 60, a(11) <= 279, a(12) <= 588, a(13) <= 9610.
%C A354068 Every orthogonal diagonal Latin square is a diagonal Latin square, so A287647(n) <= a(n) <= A360220(n) <= A287648(n). - _Eduard I. Vatutin_, Mar 03 2023
%H A354068 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 A354068 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 A354068 Eduard I. Vatutin, <a href="/A354068/a354068.txt">Proving list (best known examples)</a>.
%H A354068 <a href="/index/La#Latin">Index entries for sequences related to Latin squares and rectangles</a>.
%e A354068 One of the best orthogonal diagonal Latin squares of order n=9
%e A354068   0 1 2 3 4 5 6 7 8
%e A354068   1 2 3 8 6 4 7 0 5
%e A354068   5 4 6 0 7 8 3 1 2
%e A354068   7 3 1 5 2 6 0 8 4
%e A354068   8 7 4 6 1 2 5 3 0
%e A354068   3 0 5 4 8 7 1 2 6
%e A354068   4 6 7 2 3 0 8 5 1
%e A354068   6 5 8 1 0 3 2 4 7
%e A354068   2 8 0 7 5 1 4 6 3
%e A354068 has orthogonal diagonal mate
%e A354068   0 1 2 3 4 5 6 7 8
%e A354068   2 3 8 7 5 6 4 1 0
%e A354068   1 5 4 8 6 0 2 3 7
%e A354068   8 7 0 6 1 3 5 4 2
%e A354068   5 0 1 2 7 8 3 6 4
%e A354068   4 6 7 0 3 2 8 5 1
%e A354068   3 8 5 4 0 7 1 2 6
%e A354068   7 4 6 5 2 1 0 8 3
%e A354068   6 2 3 1 8 4 7 0 5
%e A354068 and 14 diagonal transversals, which is the minimal number, so a(9)=14.
%Y A354068 Cf. A287647, A287648, A345370, A349199, A360220.
%K A354068 nonn,more,hard
%O A354068 1,4
%A A354068 _Eduard I. Vatutin_, May 16 2022