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A354050 a(n) is the number of distinct numbers of intercalates that an orthogonal diagonal Latin square of order n can have.

%I A354050 #13 Mar 01 2025 11:16:49
%S A354050 0,0,0,1,1,0,3,26,55
%N A354050 a(n) is the number of distinct numbers of intercalates that an orthogonal diagonal Latin square of order n can have.
%C A354050 An orthogonal diagonal Latin square is a diagonal Latin square with at least one orthogonal diagonal mate. Since all orthogonal diagonal Latin squares are diagonal Latin squares, a(n) <= A345760(n).
%C A354050 a(10) >= 74, a(11) >= 76, a(12) >= 190. - updated by _Eduard I. Vatutin_, Mar 01 2025
%H A354050 Eduard I. Vatutin, <a href="https://vk.com/wall162891802_1709">About the spectra of numerical characteristics of orthogonal diagonal Latin squares of orders 1-11</a> (in Russian).
%H A354050 E. I. Vatutin, N. N. Nikitina, M. O. Manzuk, A. M. Albertyan and I. I. Kurochkin, <a href="http://evatutin.narod.ru/evatutin_spectra_t_dt_i_o_small_orders_thesis.pdf">On the construction of spectra of fast-computable numerical characteristics for diagonal Latin squares of small order</a>,  Intellectual and Information Systems (Intellect - 2021). Tula, 2021. pp. 7-17. (in Russian)
%H A354050 E. I. Vatutin, V. S. Titov, A. I. Pykhtin, A. V. Kripachev, N. N. Nikitina, M. O. Manzuk, A. M. Albertyan and I. I. Kurochkin, <a href="http://evatutin.narod.ru/evatutin_spectra_t_dt_i_o_high_orders_1.pdf">Estimation of the Cardinalities of the Spectra of Fast-computable Numerical Characteristics for Diagonal Latin Squares of Orders N>9</a> (in Russian) // Science and education in the development of industrial, social and economic spheres of Russian regions. Murom, 2022. pp. 314-315.
%H A354050 Eduard I. Vatutin, <a href="http://evatutin.narod.ru/spectra/spectra_odls_intercalates_all.png">Graphical representation of the spectra</a>.
%H A354050 Eduard I. Vatutin, Proving lists (<a href="http://evatutin.narod.ru/spectra/spectrum_odls_intercalates_n4_1_item.txt">4</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_odls_intercalates_n5_1_item.txt">5</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_odls_intercalates_n7_3_items.txt">7</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_odls_intercalates_n8_26_items.txt">8</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_odls_intercalates_n9_55_items.txt">9</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_odls_intercalates_n10_74_known_items.txt">10</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_odls_intercalates_n11_76_known_items.txt">11</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_odls_intercalates_n12_190_known_items.txt">12</a>).
%H A354050 <a href="/index/La#Latin">Index entries for sequences related to Latin squares and rectangles</a>.
%e A354050 For n=8 the number of intercalates that an orthogonal diagonal Latin square of order 8 may have is 2, 4, 8, 9, 10, 11, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 36, 40, 44, 48, 52, 56, 64, 80, or 112. Since there are 26 distinct values, a(8)=26.
%Y A354050 Cf. A345760, A349199, A350585.
%K A354050 nonn,more,hard
%O A354050 1,7
%A A354050 _Eduard I. Vatutin_, May 16 2022