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 A379665 #23 Apr 08 2025 13:09:19 %S A379665 0,0,12,9,16,25 %N A379665 Minimum number of intercalates in a Brown's diagonal Latin square of order 2n. %C A379665 A Brown's diagonal Latin square is a horizontally symmetric row-inverse or vertically symmetric column-inverse diagonal Latin square (see A339641). %C A379665 Plain symmetry diagonal Latin squares do not exist for odd orders. %C A379665 a(6)<=36, a(7)<=49, a(8)<=64, a(9)<=81, a(10)<=100, a(11)<=121, a(12)<=144, a(13)<=201, a(14)<=252. - Updated by _Eduard I. Vatutin_, Mar 01 2025 %C A379665 Hypothesis: minimum number of intercalates in Brown's diagonal Latin squares of order N=2n is equal to (N/2)^2 for N>4 (proved for N=6 and N=8 using Brute Force and for 10<=N<=24 using heuristic methods). %H A379665 Eduard I. Vatutin, <a href="https://evatutin.narod.ru/evatutin_ls_int_in_spec_type_ls.pdf">On the number of intercalates in diagonal Latin squares of special type</a>, Science and education in the development of industrial, social and economic spheres of Russian regions. Murom, 2024. pp. 284-286. (in Russian) %H A379665 Eduard I. Vatutin, <a href="https://vk.com/wall162891802_2896">About the minimum number of intercalates in Brown's diagonal Latin squares of orders N<25</a> (in Russian). %H A379665 Eduard I. Vatutin, <a href="/A379665/a379665_2.txt">Proving list (best known examples)</a> %H A379665 <a href="/La#Latin">Index entries for sequences related to Latin squares and rectangles</a>. %Y A379665 Cf. A307163, A339641. %K A379665 nonn,more,hard %O A379665 0,3 %A A379665 _Eduard I. Vatutin_, Dec 29 2024 %E A379665 a(5)=25 added by Oleg S. Zaikin and _Eduard I. Vatutin_, Apr 08 2025