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A387187 a(n) is the number of distinct numbers of transversals an extended self-orthogonal diagonal Latin square of order n.

%I A387187 #14 Sep 01 2025 22:53:12
%S A387187 1,0,0,1,1,0,4,5,244,62
%N A387187 a(n) is the number of distinct numbers of transversals an extended self-orthogonal diagonal Latin square of order n.
%C A387187 A self-orthogonal diagonal Latin square (SODLS) is a diagonal Latin square orthogonal to its transpose. An extended self-orthogonal diagonal Latin square (ESODLS) is a diagonal Latin square that has an orthogonal diagonal Latin square from the same main class. SODLS is a special case of ESODLS.
%H A387187 Eduard I. Vatutin, <a href="https://vk.com/wall162891802_2937">About the properties of ESODLS of orders 1-10 (in Russian)</a>.
%H A387187 Eduard I. Vatutin, Proving lists (<a href="https://evatutin.narod.ru/spectra/spectrum_esodls_transversals_n1_1_item.txt">1</a>, <a href="https://evatutin.narod.ru/spectra/spectrum_esodls_transversals_n4_1_item.txt">4</a>, <a href="https://evatutin.narod.ru/spectra/spectrum_esodls_transversals_n5_1_item.txt">5</a>, <a href="https://evatutin.narod.ru/spectra/spectrum_esodls_transversals_n7_4_items.txt">7</a>, <a href="https://evatutin.narod.ru/spectra/spectrum_esodls_transversals_n8_5_items.txt">8</a>, <a href="https://evatutin.narod.ru/spectra/spectrum_esodls_transversals_n9_244_items.txt">9</a>, <a href="https://evatutin.narod.ru/spectra/spectrum_esodls_transversals_n10_62_items.txt">10</a>).
%H A387187 Eduard I. Vatutin, <a href="https://evatutin.narod.ru/spectra/spectra_esodls_transversals_all.png">Graphical representation of the spectra</a>.
%H A387187 <a href="/La#Latin">Index entries for sequences related to Latin squares and rectangles</a>.
%e A387187 For n=8 the number of transversals that an extended self-orthogonal diagonal Latin square of order 7 may have is 128, 192, 224, 256, or 384. Since there are 3 distinct values, a(8)=5.
%Y A387187 Cf. A309210, A309598, A309599, A344105, A350585, A383684, A387124.
%K A387187 nonn,more,hard,new
%O A387187 1,7
%A A387187 _Eduard I. Vatutin_, Aug 21 2025