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%I #24 Aug 08 2023 22:22:28
%S 0,96,92160,290830417920
%N Number of one-plane symmetric diagonal Latin squares of order 2n.
%C One-plane symmetric diagonal Latin squares are vertically or horizontally symmetric diagonal Latin squares. a(n) is equal to 2*X-Y, where X is the number of horizontally symmetric diagonal Latin squares (sequence A292516), and Y is the number of doubly symmetric diagonal Latin squares (sequence A292517).
%H E. I. Vatutin, S. E. Kochemazov, O. S. Zaikin, V. S. Titov, <a href="http://evatutin.narod.ru/evatutin_co_ls_dls_symm_v2.pdf">Investigation of the properties of symmetric diagonal Latin squares. Corrections.</a> Intellectual and Information Systems (2017), pp. 30-36 (in Russian)
%H Eduard I. Vatutin, Stepan E. Kochemazov, Oleq S. Zaikin, Maxim O. Manzuk, Natalia N. Nikitina, Vitaly S. Titov, <a href="https://doi.org/10.25045/jpit.v10.i2.01">Central symmetry properties for diagonal Latin squares</a>, Problems of Information Technology (2019) No. 2, 3-8.
%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="/index/La#Latin">Index entries for sequences related to Latin squares and rectangles</a>
%F a(n) = 2*A292516(n) - A292517(n).
%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 A doubly symmetric diagonal Latin square:
%e 0 1 2 3 4 5 6 7
%e 3 2 7 6 1 0 5 4
%e 2 3 1 0 7 6 4 5
%e 6 7 5 4 3 2 0 1
%e 7 6 3 2 5 4 1 0
%e 4 5 0 1 6 7 2 3
%e 5 4 6 7 0 1 3 2
%e 1 0 4 5 2 3 7 6
%Y Cf. A287649, A292516, A292517, A296060, A340546.
%K nonn,more,hard
%O 1,2
%A _Eduard I. Vatutin_, Dec 04 2017
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