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 A339641 #43 Apr 04 2025 21:07:02 %S A339641 0,1,2,173,124528 %N A339641 Number of main classes of Brown's diagonal Latin squares of order 2n. %C A339641 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 A339641 Plain symmetry diagonal Latin squares do not exist for odd orders, so a(2n+1)=0. %D A339641 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 A339641 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 A339641 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 A339641 Eduard I. Vatutin, <a href="https://evatutin.narod.ru/evatutin_browns_cfs_n4-8.zip">Lists of canonical forms (4 <= N <= 8)</a>. %H A339641 <a href="/index/La#Latin">Index entries for sequences related to Latin squares and rectangles</a>. %e A339641 The diagonal Latin square %e A339641 . %e A339641 0 1 2 3 4 5 6 7 8 9 %e A339641 1 2 3 4 0 9 5 6 7 8 %e A339641 4 0 1 7 3 6 2 8 9 5 %e A339641 8 7 6 5 9 0 4 3 2 1 %e A339641 7 6 5 0 8 1 9 4 3 2 %e A339641 9 8 7 6 5 4 3 2 1 0 %e A339641 5 9 8 2 6 3 7 1 0 4 %e A339641 3 5 0 8 7 2 1 9 4 6 %e A339641 2 3 4 9 1 8 0 5 6 7 %e A339641 6 4 9 1 2 7 8 0 5 3 %e A339641 . %e A339641 is a Brown's square since it is horizontally symmetric (see A287649) and its rows form row-inverse pairs: %e A339641 . %e A339641 0 1 2 3 4 5 6 7 8 9 . . . . . . . . . . . . . . . . . . . . %e A339641 . . . . . . . . . . 1 2 3 4 0 9 5 6 7 8 . . . . . . . . . . %e A339641 . . . . . . . . . . . . . . . . . . . . 4 0 1 7 3 6 2 8 9 5 %e A339641 . . . . . . . . . . 8 7 6 5 9 0 4 3 2 1 . . . . . . . . . . %e A339641 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . %e A339641 9 8 7 6 5 4 3 2 1 0 . . . . . . . . . . . . . . . . . . . . %e A339641 . . . . . . . . . . . . . . . . . . . . 5 9 8 2 6 3 7 1 0 4 %e A339641 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . %e A339641 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . %e A339641 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . %e A339641 . %e A339641 . . . . . . . . . . . . . . . . . . . . %e A339641 . . . . . . . . . . . . . . . . . . . . %e A339641 . . . . . . . . . . . . . . . . . . . . %e A339641 . . . . . . . . . . . . . . . . . . . . %e A339641 7 6 5 0 8 1 9 4 3 2 . . . . . . . . . . %e A339641 . . . . . . . . . . . . . . . . . . . . %e A339641 . . . . . . . . . . . . . . . . . . . . %e A339641 . . . . . . . . . . 3 5 0 8 7 2 1 9 4 6 %e A339641 2 3 4 9 1 8 0 5 6 7 . . . . . . . . . . %e A339641 . . . . . . . . . . 6 4 9 1 2 7 8 0 5 3 %Y A339641 Cf. A287649, A339305, A340186. %K A339641 nonn,more,hard %O A339641 1,3 %A A339641 _Eduard I. Vatutin_, Dec 24 2020 %E A339641 a(5) added by _Eduard I. Vatutin_ from Oleg S. Zaikin, Mar 30 2025