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 A338084 #19 Apr 15 2023 10:07:03 %S A338084 1,0,2,3,20,67,596 %N A338084 Number of equivalence classes of X-based filling of diagonals in a diagonal Latin square of order 2n (or 2n+1). %C A338084 Supplemental for A309283. %C A338084 The number of solutions in an equivalence class with the main diagonal in ascending order is at most 4*2^n*n!. This maximum is only achieved for n >= 5. - _Andrew Howroyd_, Mar 27 2023 %H A338084 E. I. Vatutin, A. D. Belyshev, N. N. Nikitina, and M. O. Manzuk, <a href="http://evatutin.narod.ru/evatutin_dls_scf_gen.pdf">Use of X-based diagonal fillings and ESODLS CMS schemes for enumeration of main classes of diagonal Latin squares</a>, Telecommunications, 2023, No. 1, pp. 2-16, DOI: 10.31044/1684-2588-2023-0-1-2-16 (in Russian). %F A338084 a(n) >= A000316(n) / (4*2^n*n!). - _Andrew Howroyd_, Mar 27 2023 %e A338084 From _Andrew Howroyd_, Mar 27 2023: (Start) %e A338084 For n = 5, the following is an example solution in an equivalence class of maximum size. The second square shows the effect of swapping the two diagonals and renumbering so that the main diagonal is still in ascending order. %e A338084 0 . . . . . . . . 1 0 . . . . . . . . 1 %e A338084 . 1 . . . . . . 0 . . 1 . . . . . . 0 . %e A338084 . . 2 . . . . 3 . . . . 2 . . . . 3 . . %e A338084 . . . 3 . . 2 . . . . . . 3 . . 2 . . . %e A338084 . . . . 4 6 . . . . . . . . 4 9 . . . . %e A338084 . . . . 7 5 . . . . . . . . 6 5 . . . . %e A338084 . . . 5 . . 6 . . . . . . 4 . . 6 . . . %e A338084 . . 8 . . . . 7 . . . . 5 . . . . 7 . . %e A338084 . 9 . . . . . . 8 . . 7 . . . . . . 8 . %e A338084 4 . . . . . . . . 9 8 . . . . . . . . 9 %e A338084 (End) %Y A338084 Cf. A000316, A309283. %K A338084 nonn,more,hard %O A338084 0,3 %A A338084 _Eduard I. Vatutin_, Oct 08 2020