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A382505 a(n) is the number of distinct numbers of diagonal transversals in Brown's diagonal Latin squares of order 2n.

%I A382505 #8 Apr 03 2025 21:22:41
%S A382505 0,1,2,20,349
%N A382505 a(n) is the number of distinct numbers of diagonal transversals in Brown's diagonal Latin squares of order 2n.
%C A382505 A Brown's diagonal Latin square is a horizontally symmetric row-inverse or vertically symmetric column-inverse diagonal Latin square (see A339641).
%C A382505 Brown's diagonal Latin squares are special case of plain symmetry diagonal Latin squares that do not exist for odd orders.
%C A382505 a(6)>=1785, a(7)>=60341, a(8)>=4151.
%H A382505 Eduard I. Vatutin, <a href="https://vk.com/wall162891802_2895">About the spectra of numerical characteristics of Brown's diagonal Latin squares</a> (in Russian).
%H A382505 Eduard I. Vatutin, Proving lists (<a href="https://evatutin.narod.ru/spectra/spectrum_brown_dls_diagonal_transversals_n4_1_item.txt">4</a>, <a href="https://evatutin.narod.ru/spectra/spectrum_brown_dls_diagonal_transversals_n6_2_items.txt">6</a>, <a href="https://evatutin.narod.ru/spectra/spectrum_brown_dls_diagonal_transversals_n8_20_items.txt">8</a>, <a href="https://evatutin.narod.ru/spectra/spectrum_brown_dls_diagonal_transversals_n10_349_items.txt">10</a>).
%H A382505 Eduard I. Vatutin, <a href="https://evatutin.narod.ru/spectra/spectra_brown_dls_diagonal_transversals_all.png">Graphical representation of the spectra</a>.
%H A382505 <a href="/index/La#Latin">Index entries for sequences related to Latin squares and rectangles</a>.
%e A382505 For n=4 the number of transversals that a diagonal Latin square of order 8 may have is 0, 8, 12, 16, 18, 20, 24, 26, 28, 32, 36, 40, 44, 48, 52, 56, 64, 88, 96, or 120. Since there are 20 distinct values, a(4)=20.
%Y A382505 Cf. A339641, A344105, A381971.
%K A382505 nonn,more,hard
%O A382505 1,3
%A A382505 _Eduard I. Vatutin_, Mar 29 2025