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 A339305 #52 Apr 08 2025 13:09:15 %S A339305 0,2,128,97920,956301312 %N A339305 Number of Brown's diagonal Latin squares of order 2n with the first row in order. %C A339305 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 A339305 Plain symmetry diagonal Latin squares do not exist for odd orders, so a(2n+1)=0. %D A339305 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 A339305 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 A339305 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 A339305 Eduard I. Vatutin, <a href="https://vk.com/wall162891802_2894">Clarification for Brown's diagonal Latin squares for orders 6 and 8</a> (in Russian). %H A339305 <a href="/index/La#Latin">Index entries for sequences related to Latin squares and rectangles</a>. %F A339305 a(n) = A340186(n) / (2*n)!. - _Eduard I. Vatutin_, Jan 08 2021 %e A339305 The diagonal Latin square %e A339305 . %e A339305 0 1 2 3 4 5 6 7 8 9 %e A339305 1 2 3 4 0 9 5 6 7 8 %e A339305 4 0 1 7 3 6 2 8 9 5 %e A339305 8 7 6 5 9 0 4 3 2 1 %e A339305 7 6 5 0 8 1 9 4 3 2 %e A339305 9 8 7 6 5 4 3 2 1 0 %e A339305 5 9 8 2 6 3 7 1 0 4 %e A339305 3 5 0 8 7 2 1 9 4 6 %e A339305 2 3 4 9 1 8 0 5 6 7 %e A339305 6 4 9 1 2 7 8 0 5 3 %e A339305 . %e A339305 is a Brown's square since it is horizontally symmetric (see A287649) and its rows form row-inverse pairs: %e A339305 . %e A339305 0 1 2 3 4 5 6 7 8 9 . . . . . . . . . . . . . . . . . . . . %e A339305 . . . . . . . . . . 1 2 3 4 0 9 5 6 7 8 . . . . . . . . . . %e A339305 . . . . . . . . . . . . . . . . . . . . 4 0 1 7 3 6 2 8 9 5 %e A339305 . . . . . . . . . . 8 7 6 5 9 0 4 3 2 1 . . . . . . . . . . %e A339305 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . %e A339305 9 8 7 6 5 4 3 2 1 0 . . . . . . . . . . . . . . . . . . . . %e A339305 . . . . . . . . . . . . . . . . . . . . 5 9 8 2 6 3 7 1 0 4 %e A339305 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . %e A339305 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . %e A339305 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . %e A339305 . %e A339305 . . . . . . . . . . . . . . . . . . . . %e A339305 . . . . . . . . . . . . . . . . . . . . %e A339305 . . . . . . . . . . . . . . . . . . . . %e A339305 . . . . . . . . . . . . . . . . . . . . %e A339305 7 6 5 0 8 1 9 4 3 2 . . . . . . . . . . %e A339305 . . . . . . . . . . . . . . . . . . . . %e A339305 . . . . . . . . . . . . . . . . . . . . %e A339305 . . . . . . . . . . 3 5 0 8 7 2 1 9 4 6 %e A339305 2 3 4 9 1 8 0 5 6 7 . . . . . . . . . . %e A339305 . . . . . . . . . . 6 4 9 1 2 7 8 0 5 3 %Y A339305 Cf. A287649, A339641, A340186, A379145. %K A339305 nonn,more,hard %O A339305 1,2 %A A339305 _Eduard I. Vatutin_, Dec 24 2020 %E A339305 a(3) corrected by _Eduard I. Vatutin_ and Oleg Zaikin, Dec 16 2024 %E A339305 a(5) added by Oleg S. Zaikin and _Eduard I. Vatutin_, Apr 08 2025