Maximum number of intercalates in a diagonal Latin square of order n, https://oeis.org/A307164 n=1, a(1)=0 Article: Vatutin E., Belyshev A., Nikitina N., Manzuk M. Evaluation of Efficiency of Using Simple Transformations When Searching for Orthogonal Diagonal Latin Squares of Order 10 // Communications in Computer and Information Science. Vol. 1304. Springer, 2020. pp. 127-146. DOI: 10.1007/978-3-030-66895-2_9 Way of finding: brute force 0 n=2, a(2)=0 - n=3, a(3)=0 - n=4, a(4)=12 Article: Vatutin E., Belyshev A., Nikitina N., Manzuk M. Evaluation of Efficiency of Using Simple Transformations When Searching for Orthogonal Diagonal Latin Squares of Order 10 // Communications in Computer and Information Science. Vol. 1304. Springer, 2020. pp. 127-146. DOI: 10.1007/978-3-030-66895-2_9 Way of finding: brute force 0 1 2 3 3 2 1 0 1 0 3 2 2 3 0 1 n=5, a(5)=4 Article: Vatutin E., Belyshev A., Nikitina N., Manzuk M. Evaluation of Efficiency of Using Simple Transformations When Searching for Orthogonal Diagonal Latin Squares of Order 10 // Communications in Computer and Information Science. Vol. 1304. Springer, 2020. pp. 127-146. DOI: 10.1007/978-3-030-66895-2_9 Way of finding: brute force 0 1 2 3 4 4 2 0 1 3 1 4 3 2 0 3 0 1 4 2 2 3 4 0 1 n=6, a(6)=9 Article: Vatutin E., Belyshev A., Nikitina N., Manzuk M. Evaluation of Efficiency of Using Simple Transformations When Searching for Orthogonal Diagonal Latin Squares of Order 10 // Communications in Computer and Information Science. Vol. 1304. Springer, 2020. pp. 127-146. DOI: 10.1007/978-3-030-66895-2_9 Way of finding: brute force 0 1 2 3 4 5 4 2 5 0 3 1 3 5 1 2 0 4 5 3 0 4 1 2 2 4 3 1 5 0 1 0 4 5 2 3 n=7, a(7)=30 Article: Vatutin E., Belyshev A., Nikitina N., Manzuk M. Evaluation of Efficiency of Using Simple Transformations When Searching for Orthogonal Diagonal Latin Squares of Order 10 // Communications in Computer and Information Science. Vol. 1304. Springer, 2020. pp. 127-146. DOI: 10.1007/978-3-030-66895-2_9 Way of finding: brute force 0 1 2 3 4 5 6 4 2 6 5 0 1 3 3 6 1 0 5 2 4 6 3 5 4 1 0 2 1 5 3 2 6 4 0 5 0 4 6 2 3 1 2 4 0 1 3 6 5 n=8, a(8)=112 Article: Vatutin E., Belyshev A., Nikitina N., Manzuk M. Evaluation of Efficiency of Using Simple Transformations When Searching for Orthogonal Diagonal Latin Squares of Order 10 // Communications in Computer and Information Science. Vol. 1304. Springer, 2020. pp. 127-146. DOI: 10.1007/978-3-030-66895-2_9 Way of finding: brute force 0 1 2 3 4 5 6 7 4 2 1 7 0 6 5 3 5 7 3 2 6 0 4 1 7 5 6 4 3 1 2 0 6 3 7 1 5 4 0 2 1 0 4 6 2 7 3 5 3 6 5 0 7 2 1 4 2 4 0 5 1 3 7 6 n=9, a(9)=72 Article: Vatutin E., Belyshev A., Nikitina N., Manzuk M. Evaluation of Efficiency of Using Simple Transformations When Searching for Orthogonal Diagonal Latin Squares of Order 10 // Communications in Computer and Information Science. Vol. 1304. Springer, 2020. pp. 127-146. DOI: 10.1007/978-3-030-66895-2_9 Way of finding: brute force using X-based fillings 0 1 2 3 4 5 6 7 8 6 8 3 4 7 2 0 5 1 5 7 6 1 8 0 2 4 3 7 3 8 2 5 4 1 0 6 2 4 0 8 1 3 5 6 7 4 5 1 6 0 7 3 8 2 8 6 7 5 3 1 4 2 0 1 0 5 7 2 6 8 3 4 3 2 4 0 6 8 7 1 5 n=10, a(10)>=93 Announcement: https://vk.com/wall162891802_1540, Eduard I. Vatutin, Feb 02 2021 Way of finding: random search 0 8 6 5 7 1 2 9 4 3 9 1 7 4 6 8 3 0 5 2 4 3 2 9 5 0 1 8 6 7 1 9 4 3 2 6 7 5 0 8 5 2 3 0 4 9 8 1 7 6 3 7 8 1 0 5 9 6 2 4 8 0 5 2 3 7 6 4 9 1 2 6 1 8 9 4 0 7 3 5 7 4 9 6 1 3 5 2 8 0 6 5 0 7 8 2 4 3 1 9 n=11, a(11)>=94 Announcement: https://vk.com/wall162891802_1549, Eduard I. Vatutin, Mar 03 2021 Way of finding: random search 0 1 2 3 4 5 6 7 8 9 10 2 3 0 1 5 6 8 10 9 4 7 5 6 10 8 0 2 1 9 3 7 4 10 8 7 9 6 4 3 2 1 0 5 1 0 9 2 7 8 5 4 10 6 3 3 9 4 10 2 1 0 6 7 5 8 8 10 6 7 9 3 4 0 5 2 1 9 2 1 0 8 7 10 5 4 3 6 7 4 8 5 1 0 2 3 6 10 9 4 7 5 6 3 10 9 1 2 8 0 6 5 3 4 10 9 7 8 0 1 2 n=12, a(12)>=252 Announcement: https://vk.com/wall162891802_1712, Eduard I. Vatutin, Jul 28 2021 Way of finding: random search in the neighborhood of central symmetry + combinatorial structures ODLS CFs analysis 0 1 2 3 4 5 6 7 8 9 10 11 1 2 0 4 5 3 8 6 7 11 9 10 3 5 4 0 2 1 10 9 11 7 6 8 9 10 11 6 7 8 3 4 5 0 1 2 10 11 9 7 8 6 5 3 4 2 0 1 6 8 7 9 11 10 1 0 2 4 3 5 2 0 1 5 3 4 7 8 6 10 11 9 4 3 5 1 0 2 9 11 10 6 8 7 5 4 3 2 1 0 11 10 9 8 7 6 11 9 10 8 6 7 4 5 3 1 2 0 7 6 8 10 9 11 0 2 1 3 5 4 8 7 6 11 10 9 2 1 0 5 4 3 n=13, a(13)>=156 Announcement: https://vk.com/wall162891802_1904, Eduard I. Vatutin, Jan 23 2022 Way of finding: expanding spectrum using 1 intercalate/loop neighborhoods based improvement 0 1 2 3 4 5 6 7 8 9 10 11 12 2 3 0 4 1 6 5 8 12 10 11 9 7 4 7 1 8 0 12 9 2 10 6 3 5 11 5 11 4 12 9 8 10 6 0 2 7 1 3 11 6 12 0 8 9 1 5 4 7 2 3 10 3 2 7 11 5 10 8 1 6 12 4 0 9 1 10 5 9 6 2 11 12 7 3 0 4 8 8 12 6 2 7 0 3 4 5 11 9 10 1 12 8 11 7 10 4 0 3 9 1 5 2 6 10 0 3 6 12 7 2 9 11 5 1 8 4 9 4 8 1 3 11 7 10 2 0 6 12 5 6 5 9 10 2 1 12 11 3 4 8 7 0 7 9 10 5 11 3 4 0 1 8 12 6 2 n=14, a(14)>=353 Announcement: https://vk.com/wall162891802_2475, Eduard I. Vatutin, Aug 06 2023 Way of finding: neighborhoods of different special types of DLS 0 1 2 3 4 5 6 7 8 9 10 11 12 13 12 13 4 7 2 10 5 8 3 11 6 9 0 1 7 5 10 11 12 4 13 0 9 1 2 3 8 6 8 6 13 9 10 2 1 12 11 3 4 0 7 5 11 10 5 12 6 13 4 9 0 7 1 8 3 2 5 7 0 4 3 11 12 1 2 10 9 13 6 8 13 12 11 10 9 8 7 6 5 4 3 2 1 0 2 3 8 1 7 0 9 4 13 6 12 5 10 11 3 9 6 0 5 1 2 11 12 8 13 7 4 10 1 0 9 6 11 3 8 5 10 2 7 4 13 12 4 11 1 5 0 7 3 10 6 13 8 12 2 9 9 2 12 8 13 6 10 3 7 0 5 1 11 4 6 8 3 2 1 9 0 13 4 12 11 10 5 7 10 4 7 13 8 12 11 2 1 5 0 6 9 3 Aug 06 2023