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A345760 a(n) is the number of distinct numbers of intercalates of order n diagonal Latin squares.

%I A345760 #59 Mar 02 2025 08:03:01
%S A345760 0,0,0,1,2,1,21,61,64
%N A345760 a(n) is the number of distinct numbers of intercalates of order n diagonal Latin squares.
%C A345760 a(n) <= A307164(n) - A307163(n) + 1.
%C A345760 a(n) <= A287764(n).
%C A345760 a(10) >= 98, a(11) >= 145, a(12) >= 259, a(13) >= 200, a(14) >= 362, a(15) >= 536, a(16) >= 792, a(17) >= 685, a(18) >= 535, a(19) >= 447, a(20) >= 1011, a(21) >= 747, a(22) >= 872, a(23) >= 885, a(24) >= 1610, a(25) >= 1677, a(26) >= 1266, a(27) >= 1337, a(28) >= 2795. - _Eduard I. Vatutin_, Oct 02 2021, updated Mar 02 2025
%H A345760 Eduard I. Vatutin, <a href="https://vk.com/wall162891802_1678">About the spectra of numerical characteristics of diagonal Latin squares of orders 1-7</a> (in Russian).
%H A345760 Eduard I. Vatutin, <a href="https://vk.com/wall162891802_1698">About the spectra of numerical characteristics of diagonal Latin squares of order 8</a> (in Russian).
%H A345760 Eduard I. Vatutin, <a href="https://vk.com/wall162891802_1708">About the approximation of spectra of numerical characteristics of diagonal Latin squares of order 9</a> (in Russian).
%H A345760 Eduard I. Vatutin, <a href="https://vk.com/wall162891802_2100">About the results of experiment with spectra of diagonal Latin squares using Brute Force and distributed computing projects Gerasim@Home and RakeSearch</a> (in Russian).
%H A345760 Eduard I. Vatutin, <a href="http://evatutin.narod.ru/spectra/spectra_dls_intercalates_all.png">Graphical representation of the spectra</a>.
%H A345760 Eduard I. Vatutin, Proving lists (<a href="http://evatutin.narod.ru/spectra/spectrum_dls_intercalates_n1_0_items.txt">1</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_dls_intercalates_n4_1_item.txt">4</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_dls_intercalates_n5_2_items.txt">5</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_dls_intercalates_n6_1_item.txt">6</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_dls_intercalates_n7_21_items.txt">7</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_dls_intercalates_n8_61_items.txt">8</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_dls_intercalates_n9_64_items.txt">9</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_dls_intercalates_n10_98_known_items.txt">10</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_dls_intercalates_n11_145_known_items.txt">11</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_dls_intercalates_n12_259_known_items.txt">12</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_dls_intercalates_n13_200_known_items.txt">13</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_dls_intercalates_n14_362_known_items.txt">14</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_dls_intercalates_n15_536_known_items.txt">15</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_dls_intercalates_n16_792_known_items.txt">16</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_dls_intercalates_n17_685_known_items.txt">17</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_dls_intercalates_n18_535_known_items.txt">18</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_dls_intercalates_n19_447_known_items.txt">19</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_dls_intercalates_n20_1011_known_items.txt">20</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_dls_intercalates_n21_747_known_items.txt">21</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_dls_intercalates_n22_872_known_items.txt">22</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_dls_intercalates_n23_883_known_items.txt">23</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_dls_intercalates_n24_1610_known_items.txt">24</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_dls_intercalates_n25_1677_known_items.txt">25</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_dls_intercalates_n26_1266_known_items.txt">26</a>).
%H A345760 E. I. Vatutin, N. N. Nikitina, M. O. Manzuk, I. I. Kurochkin, A. M. Albertyan, A. V. Kripachev, A. I. Pykhtin, <a href="http://evatutin.narod.ru/evatutin_dls_heur_spectra_method_2.pdf">Methods for getting spectra of fast computable numerical characteristics of diagonal Latin squares</a>, Cloud and distributed computing systems in electronic control conference, within the National supercomputing forum (NSCF - 2022). Pereslavl-Zalessky, 2023. pp. 19-23. (in Russian)
%H A345760 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 A345760 E. I. Vatutin, V. S. Titov, A. I. Pykhtin, A. V. Kripachev, N. N. Nikitina, M. O. Manzuk, A. M. Albertyan, I. I. Kurochkin, <a href="http://evatutin.narod.ru/evatutin_dls_heur_spectra_method.pdf">Heuristic method for getting approximations of spectra of numerical characteristics for diagonal Latin squares</a>, Intellectual information systems: trends, problems, prospects, Kursk, 2022. pp. 35-41. (in Russian)
%H A345760 <a href="https://oeis.org/index/La#Latin">Index entries for sequences related to Latin squares and rectangles</a>.
%e A345760 For n=7 the number of intercalates that a diagonal Latin square of order 7 may have is 0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 22, 26, or 30. Since there are 21 distinct values, a(7)=21.
%Y A345760 Cf. A287764, A307163, A307164, A309344, A344105, A345370, A345761.
%K A345760 nonn,more,hard
%O A345760 1,5
%A A345760 _Eduard I. Vatutin_, Jun 26 2021
%E A345760 a(9) added by _Eduard I. Vatutin_, Oct 22 2022