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A382957 a(n) is the number of distinct numbers of intercalates in an extended self-orthogonal diagonal Latin squares of order n.

%I A382957 #13 Aug 23 2025 14:44:44
%S A382957 1,0,0,1,1,0,3,8,52,45
%N A382957 a(n) is the number of distinct numbers of intercalates in an extended self-orthogonal diagonal Latin squares of order n.
%C A382957 A self-orthogonal diagonal Latin square (SODLS, see A329685) is a diagonal Latin square orthogonal to its transpose. An extended self-orthogonal diagonal Latin square (ESODLS, see A309210) 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 A382957 Eduard I. Vatutin, Proving lists (<a href="https://evatutin.narod.ru/spectra/spectrum_esodls_intercalates_n1_1_item.txt">1</a>, <a href="https://evatutin.narod.ru/spectra/spectrum_esodls_intercalates_n4_1_item.txt">4</a>, <a href="https://evatutin.narod.ru/spectra/spectrum_esodls_intercalates_n5_1_item.txt">5</a>, <a href="https://evatutin.narod.ru/spectra/spectrum_esodls_intercalates_n7_3_items.txt">7</a>, <a href="https://evatutin.narod.ru/spectra/spectrum_esodls_intercalates_n8_6_items.txt">8</a>, <a href="https://evatutin.narod.ru/spectra/spectrum_esodls_intercalates_n9_52_items.txt">9</a>, <a href="https://evatutin.narod.ru/spectra/spectrum_esodls_intercalates_n10_45_items.txt">10</a>).
%H A382957 Eduard I. Vatutin, <a href="https://evatutin.narod.ru/spectra/spectra_esodls_intercalates_all.png">Graphical representation of the spectra</a>.
%H A382957 Eduard I. Vatutin, <a href="https://vk.com/wall162891802_2937">About the properties of ESODLS of orders 1-10</a> (in Russian).
%H A382957 <a href="/index/La#Latin">Index entries for sequences related to Latin squares and rectangles</a>.
%e A382957 For n=7 the number of intercalates that an extended self-orthogonal diagonal Latin square of order 7 may have is 0, 10, or 18. Since there are 3 distinct values, a(7)=3.
%Y A382957 Cf. A309210, A309598, A309599, A329685, A345760, A382952.
%K A382957 nonn,more,hard,changed
%O A382957 1,7
%A A382957 _Eduard I. Vatutin_, Apr 10 2025