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 A299784 #92 Aug 24 2025 04:17:47 %S A299784 1,0,0,2,4,96,192,1536,1536,15360,15360,184320,184320,2580480,2580480 %N A299784 Maximum size of a main class for diagonal Latin squares of order n with the first row in ascending order. %C A299784 a(n) <= 2^m * m! * 4, where m = floor(n/2). %C A299784 It seems that a(n) = 2^m * m! * 4 for all n > 6. - _Eduard I. Vatutin_, Jun 08 2020 %C A299784 0 <= A299783(n) <= a(n). - _Eduard I. Vatutin_, Jun 08 2020 %H A299784 E. Vatutin, A. Belyshev, S. Kochemazov, O. Zaikin, and N. Nikitina, <a href="http://evatutin.narod.ru/evatutin_co_dls_cfs_cnt.pdf">Enumeration of isotopy classes of diagonal Latin squares of small order using volunteer computing</a>, Supercomputing Days Russia 2018, Moscow, Moscow State University, 2018, pp. 933-942. %H A299784 E. Vatutin, A. Belyshev, S. Kochemazov, O. Zaikin, and N. Nikitina, <a href="https://doi.org/10.1007/978-3-030-05807-4_49">Enumeration of isotopy classes of diagonal Latin squares of small order using volunteer computing</a>, Communications in Computer and Information Science. Vol. 965. Springer, 2018. pp. 578-586. %H A299784 E. I. Vatutin, <a href="https://vk.com/wall162891802_1103">Discussion about properties of diagonal Latin squares</a> (in Russian). %H A299784 E. I. Vatutin, <a href="https://vk.com/wall162891802_1106">About the maximal size of main class for diagonal Latin squares of orders 11-15</a> (in Russian). %H A299784 Eduard I. Vatutin, <a href="http://evatutin.narod.ru/evatutin_dls_mc_max_card_9_to_15.pdf">Estimating the maximal size of main class for diagonal Latin squares of orders 9-15</a>, Medical-Ecological and Information Technologies - 2020, Part 2, 2020, pp. 57-62. (in Russian) %H A299784 Eduard I. Vatutin, <a href="https://vk.com/wall162891802_1575">About the relationship between the minimal and maximal cardinality of main classes for diagonal Latin squares</a> (in Russian). %H A299784 Eduard I. Vatutin, <a href="/A299784/a299784.txt">Proving list (best known examples)</a>. %H A299784 <a href="/index/La#Latin">Index entries for sequences related to Latin squares and rectangles</a>. %F A299784 a(n) = A299787(n) / n!. %F A299784 From _Eduard I. Vatutin_, May 30 2021: (Start) %F A299784 A299783(n) = a(n) for 1 <= n <= 5. %F A299784 A299783(6)*3 = a(6). %F A299784 A299783(7)*6 = a(7). %F A299784 A299783(8)*16 = a(8). %F A299784 A299783(9)*32 <= a(9). %F A299784 A299783(10)*10 <= a(10). %F A299784 A299783(11)*10 <= a(11). %F A299784 A299783(12)*4 <= a(12). %F A299784 A299783(13)*24 <= a(13). (End) %e A299784 From _Eduard I. Vatutin_, May 30 2021: (Start) %e A299784 The following DLS of order 9 has a main class with cardinality 1536: %e A299784 0 1 2 3 4 5 6 7 8 %e A299784 1 2 0 4 8 6 5 3 7 %e A299784 7 4 5 8 0 3 2 6 1 %e A299784 5 8 7 6 1 0 3 2 4 %e A299784 8 0 3 2 7 1 4 5 6 %e A299784 3 7 8 5 6 4 1 0 2 %e A299784 6 3 1 7 5 2 8 4 0 %e A299784 2 6 4 0 3 8 7 1 5 %e A299784 4 5 6 1 2 7 0 8 3 %e A299784 The following DLS of order 10 has a main class with cardinality 15360: %e A299784 0 1 2 3 4 5 6 7 8 9 %e A299784 1 2 0 4 5 3 9 8 6 7 %e A299784 3 5 6 1 8 7 4 0 9 2 %e A299784 9 4 7 8 3 2 1 6 0 5 %e A299784 2 7 3 0 9 8 5 1 4 6 %e A299784 6 8 5 9 2 4 7 3 1 0 %e A299784 4 6 9 7 0 1 3 2 5 8 %e A299784 7 0 4 6 1 9 8 5 2 3 %e A299784 8 3 1 5 6 0 2 9 7 4 %e A299784 5 9 8 2 7 6 0 4 3 1 %e A299784 (End) %Y A299784 Cf. A287764, A299783. %K A299784 nonn,more,hard,changed %O A299784 1,4 %A A299784 _Eduard I. Vatutin_, Jan 21 2019 %E A299784 a(9)-a(10) from _Eduard I. Vatutin_, Mar 15 2020 %E A299784 a(11)-a(15) from _Eduard I. Vatutin_, Jun 08 2020