This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A340186 #25 Apr 07 2025 20:38:30 %S A340186 0,48,184320,3948134400,3470226200985600 %N A340186 Number of Brown's diagonal Latin squares of order 2n. %C A340186 A Brown's diagonal Latin square is a horizontally symmetric row-inverse or vertically symmetric column-inverse diagonal Latin square. Diagonal Latin squares of this type have interesting properties, for example, a large number of transversals. %C A340186 Plain symmetry diagonal Latin squares do not exist for odd orders, so a(2n+1)=0. %D A340186 J. W. Brown, F. Cherry, L. Most, M. Most, E. T. Parker, W. D. Wallis, Completion of the spectrum of orthogonal diagonal Latin squares, Lecture notes in pure and applied mathematics, 1992, Vol. 139, pp. 43-49. %H A340186 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 A340186 Eduard I. Vatutin, <a href="https://vk.com/wall162891802_1471">Enumeration of the Brown's diagonal Latin squares of orders 1-9</a> (in Russian). %H A340186 <a href="/index/La#Latin">Index entries for sequences related to Latin squares and rectangles</a>. %F A340186 a(n) = A339305(n) * (2*n)!. %e A340186 The diagonal Latin square %e A340186 . %e A340186 0 1 2 3 4 5 6 7 8 9 %e A340186 1 2 3 4 0 9 5 6 7 8 %e A340186 4 0 1 7 3 6 2 8 9 5 %e A340186 8 7 6 5 9 0 4 3 2 1 %e A340186 7 6 5 0 8 1 9 4 3 2 %e A340186 9 8 7 6 5 4 3 2 1 0 %e A340186 5 9 8 2 6 3 7 1 0 4 %e A340186 3 5 0 8 7 2 1 9 4 6 %e A340186 2 3 4 9 1 8 0 5 6 7 %e A340186 6 4 9 1 2 7 8 0 5 3 %e A340186 . %e A340186 is a Brown's square since it is horizontally symmetric (see A287649) and its rows form row-inverse pairs: %e A340186 . %e A340186 0 1 2 3 4 5 6 7 8 9 . . . . . . . . . . . . . . . . . . . . %e A340186 . . . . . . . . . . 1 2 3 4 0 9 5 6 7 8 . . . . . . . . . . %e A340186 . . . . . . . . . . . . . . . . . . . . 4 0 1 7 3 6 2 8 9 5 %e A340186 . . . . . . . . . . 8 7 6 5 9 0 4 3 2 1 . . . . . . . . . . %e A340186 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . %e A340186 9 8 7 6 5 4 3 2 1 0 . . . . . . . . . . . . . . . . . . . . %e A340186 . . . . . . . . . . . . . . . . . . . . 5 9 8 2 6 3 7 1 0 4 %e A340186 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . %e A340186 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . %e A340186 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . %e A340186 . %e A340186 . . . . . . . . . . . . . . . . . . . . %e A340186 . . . . . . . . . . . . . . . . . . . . %e A340186 . . . . . . . . . . . . . . . . . . . . %e A340186 . . . . . . . . . . . . . . . . . . . . %e A340186 7 6 5 0 8 1 9 4 3 2 . . . . . . . . . . %e A340186 . . . . . . . . . . . . . . . . . . . . %e A340186 . . . . . . . . . . . . . . . . . . . . %e A340186 . . . . . . . . . . 3 5 0 8 7 2 1 9 4 6 %e A340186 2 3 4 9 1 8 0 5 6 7 . . . . . . . . . . %e A340186 . . . . . . . . . . 6 4 9 1 2 7 8 0 5 3 %Y A340186 Cf. A339305, A339641. %K A340186 nonn,more,hard %O A340186 1,2 %A A340186 _Eduard I. Vatutin_, Dec 31 2020 %E A340186 a(3) corrected by _Eduard I. Vatutin_ and Oleg Zaikin, Jan 12 2025 %E A340186 a(5) added by _Eduard I. Vatutin_ and Oleg S. Zaikin, Apr 02 2025