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%I #23 Oct 22 2023 12:37:43
%S 0,1,2,9717
%N Number of main classes of diagonal Latin squares of order 2n that contain a one-plane symmetric square.
%C A one-plane symmetric diagonal Latin square is a vertically or horizontally symmetric diagonal Latin square (see A296060). Such diagonal Latin squares do not exist for odd orders > 1.
%H Eduard I. Vatutin, <a href="https://vk.com/wall162891802_1470">On the number of main classes of one plane and double plane symmetric diagonal Latin squares of orders 1-8</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 <a href="https://oeis.org/index/La#Latin">Index entries for sequences related to Latin squares and rectangles</a>.
%e A horizontally symmetric diagonal Latin square:
%e 0 1 2 3 4 5
%e 4 2 0 5 3 1
%e 5 4 3 2 1 0
%e 2 5 4 1 0 3
%e 3 0 1 4 5 2
%e 1 3 5 0 2 4
%e A vertically symmetric diagonal Latin square:
%e 0 1 2 3 4 5
%e 4 2 5 0 3 1
%e 3 5 1 2 0 4
%e 5 3 0 4 1 2
%e 2 4 3 1 5 0
%e 1 0 4 5 2 3
%e Both are one-plane symmetric diagonal Latin squares.
%Y Cf. A287649, A287764, A292516, A293777, A293778, A296060, A296061, A340550.
%K nonn,more,hard,bref
%O 1,3
%A _Eduard I. Vatutin_, Jan 11 2021
%E Name clarified by _Andrew Howroyd_, Oct 22 2023