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A368182 a(n) is the number of distinct numbers of intercalates in Latin squares of order n.

%I A368182 #35 Jun 26 2025 07:31:25
%S A368182 1,1,1,2,2,9,23,61
%N A368182 a(n) is the number of distinct numbers of intercalates in Latin squares of order n.
%C A368182 a(9)>=64, a(10)>=103, a(11)>=145, a(12)>=259, a(13)>=200, a(14)>=362, a(15)>=536, a(16)>=794, a(17)>=705, a(18)>=655, a(19)>=469, a(20)>=1362, a(21)>=985, a(22)>=1435, a(23)>=967, a(24)>=1754, a(25)>=1679, a(26)>=2040, a(28)>=2803. - _Eduard I. Vatutin_, added Aug 13 2024, updated Jun 25 2025
%H A368182 Eduard I. Vatutin, <a href="https://vk.com/wall162891802_2635">About the intercalates spectra in a Latin squares of orders 1-8</a> (in Russian).
%H A368182 Eduard I. Vatutin, <a href="https://evatutin.narod.ru/spectra/spectra_ls_intercalates_all.png">Graphical representation of the spectra</a>.
%H A368182 Eduard I. Vatutin, Proving lists (<a href="http://evatutin.narod.ru/spectra/spectrum_ls_intercalates_n1_1_item.txt">1</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_ls_intercalates_n2_1_item.txt">2</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_ls_intercalates_n3_1_item.txt">3</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_ls_intercalates_n4_2_items.txt">4</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_ls_intercalates_n5_2_items.txt">5</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_ls_intercalates_n6_9_items.txt">6</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_ls_intercalates_n7_23_items.txt">7</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_ls_intercalates_n8_61_items.txt">8</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_ls_intercalates_n9_64_known_items.txt">9</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_ls_intercalates_n10_103_known_items.txt">10</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_ls_intercalates_n11_145_known_items.txt">11</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_ls_intercalates_n12_259_known_items.txt">12</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_ls_intercalates_n13_200_known_items.txt">13</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_ls_intercalates_n14_362_known_items.txt">14</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_ls_intercalates_n15_536_known_items.txt">15</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_ls_intercalates_n16_794_known_items.txt">16</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_ls_intercalates_n17_705_known_items.txt">17</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_ls_intercalates_n18_655_known_items.txt">18</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_ls_intercalates_n19_469_known_items.txt">19</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_ls_intercalates_n20_1362_known_items.txt">20</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_ls_intercalates_n21_985_known_items.txt">21</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_ls_intercalates_n22_1435_known_items.txt">22</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_ls_intercalates_n23_967_known_items.txt">23</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_ls_intercalates_n24_1754_known_items.txt">24</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_ls_intercalates_n25_1679_known_items.txt">25</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_ls_intercalates_n26_2040_known_items.txt">26</a>, <a href="http://evatutin.narod.ru/spectra/spectrum_ls_intercalates_n28_2803_known_items.txt">28</a>).
%H A368182 <a href="/index/La#Latin">Index entries for sequences related to Latin squares and rectangles</a>.
%e A368182 For n=7, a Latin square of order 7 may have 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 22, 26, 30, or 42 intercalates. There are 23 possibilities, so a(7)=23.
%Y A368182 Cf. A092237, A309344, A345760.
%K A368182 nonn,more,hard
%O A368182 1,4
%A A368182 _Eduard I. Vatutin_, Feb 15 2024