Minimum number of intercalates in a diagonal Latin square of order n, https://oeis.org/A307163 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)=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 1 2 3 4 4 2 3 0 1 3 4 1 2 0 1 3 0 4 2 2 0 4 1 3 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)=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 1 2 3 4 5 6 4 2 6 0 5 1 3 3 5 1 6 0 4 2 5 6 3 4 1 2 0 6 4 5 2 3 0 1 1 3 0 5 2 6 4 2 0 4 1 6 3 5 n=8, a(8)=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 1 2 3 4 5 6 7 3 2 5 1 6 7 0 4 6 4 1 0 7 2 5 3 2 7 3 4 5 0 1 6 7 5 0 6 3 4 2 1 5 0 4 7 1 6 3 2 4 3 6 5 2 1 7 0 1 6 7 2 0 3 4 5 n=9, a(9)=0 Announcement: https://vk.com/wall162891802_1333, Eduard I. Vatutin, Sep 10 2020 Way of finding: brute force using X-based fillings 0 2 3 4 5 6 7 8 1 5 1 4 7 8 3 2 0 6 8 7 2 5 6 1 3 4 0 6 5 8 3 7 2 0 1 4 2 6 0 8 4 7 1 5 3 4 0 7 6 1 5 8 3 2 3 4 5 1 0 8 6 2 7 1 8 6 2 3 0 4 7 5 7 3 1 0 2 4 5 6 8 n=10, a(10)=0 Announcement: https://vk.com/wall162891802_1531, Eduard I. Vatutin, Jan 28 2021 Way of finding: random search 0 6 4 9 2 3 7 8 5 1 5 1 8 4 7 9 3 6 2 0 3 0 2 7 9 1 8 4 6 5 6 5 0 3 1 8 9 2 4 7 7 2 9 5 4 6 1 3 0 8 1 9 6 8 3 5 4 0 7 2 2 8 7 0 5 4 6 9 1 3 4 3 5 1 8 0 2 7 9 6 9 7 3 6 0 2 5 1 8 4 8 4 1 2 6 7 0 5 3 9 n=11, a(11)=0 Announcement: -, Eduard I. Vatutin, Jan 23 2021 Way of finding: cyclic diagonal Latin squares 0 1 2 3 4 5 6 7 8 9 10 2 3 4 5 1 7 8 9 10 6 0 3 9 5 6 7 8 2 10 4 0 1 5 6 7 8 9 10 4 0 1 2 3 6 0 8 2 10 4 5 1 7 3 9 8 2 10 4 0 1 7 3 9 5 6 10 4 0 1 2 3 9 5 6 7 8 4 5 1 7 3 9 10 6 0 8 2 1 7 3 9 5 6 0 8 2 10 4 7 8 9 10 6 0 1 2 3 4 5 9 10 6 0 8 2 3 4 5 1 7 n=12, a(12)=0 Announcement: https://vk.com/wall162891802_1618, Eduard I. Vatutin, Mar 29 2021 Way of finding: neighborhoods of centrally symmetric squares 0 1 2 3 4 5 6 7 8 9 10 11 7 3 8 5 6 4 2 9 0 11 1 10 9 8 11 0 1 7 5 6 10 3 2 4 10 4 9 7 0 6 1 5 2 8 11 3 11 7 0 9 2 1 10 4 3 6 5 8 1 9 10 11 5 8 7 2 4 0 3 6 3 6 1 8 10 9 4 11 5 2 7 0 4 11 3 6 8 2 0 10 7 1 9 5 6 5 4 10 11 0 3 1 9 7 8 2 8 10 6 2 3 11 9 0 1 5 4 7 2 0 5 1 7 10 8 3 11 4 6 9 5 2 7 4 9 3 11 8 6 10 0 1 n=13, a(13)=0 Announcement: -, Eduard I. Vatutin, Mar 29 2021 Way of finding: cyclic diagonal Latin squares 0 1 2 3 4 5 6 7 8 9 10 11 12 2 3 4 5 6 7 8 9 10 11 12 0 1 4 5 6 7 8 9 10 11 12 0 1 2 3 6 7 8 9 10 11 12 0 1 2 3 4 5 8 9 10 11 12 0 1 2 3 4 5 6 7 10 11 12 0 1 2 3 4 5 6 7 8 9 12 0 1 2 3 4 5 6 7 8 9 10 11 1 2 3 4 5 6 7 8 9 10 11 12 0 3 4 5 6 7 8 9 10 11 12 0 1 2 5 6 7 8 9 10 11 12 0 1 2 3 4 7 8 9 10 11 12 0 1 2 3 4 5 6 9 10 11 12 0 1 2 3 4 5 6 7 8 11 12 0 1 2 3 4 5 6 7 8 9 10 n=14, a(14)<=3 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 3 2 6 1 5 13 12 9 7 8 4 0 11 10 6 12 7 5 0 9 3 13 2 11 8 1 10 4 8 4 3 12 11 7 13 0 1 2 9 10 6 5 9 5 12 0 10 2 1 4 11 3 6 13 8 7 7 9 0 11 2 6 10 5 12 13 3 8 4 1 2 7 10 4 13 12 5 8 3 0 1 6 9 11 1 8 13 10 9 4 7 11 6 12 5 2 3 0 13 11 8 6 12 10 4 3 9 1 7 5 0 2 10 13 11 8 6 3 0 1 5 4 12 7 2 9 11 6 9 2 3 1 8 10 0 5 13 4 7 12 12 10 5 9 1 8 11 2 4 7 0 3 13 6 5 0 4 7 8 11 9 6 13 10 2 12 1 3 4 3 1 13 7 0 2 12 10 6 11 9 5 8 n=15, a(15)=0 Announcement: https://vk.com/wall162891802_2476, Eduard I. Vatutin, Aug 06 2023 Way of finding: diagonalized cyclic DLS 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 0 4 5 3 7 13 9 14 11 12 10 6 8 10 11 12 13 6 7 1 2 4 5 9 14 8 0 3 13 6 7 14 8 9 4 5 12 10 0 1 2 3 11 5 3 4 10 11 12 14 8 1 2 7 13 6 9 0 12 10 11 7 13 6 0 1 3 4 8 9 14 2 5 3 4 5 11 12 10 8 9 2 0 13 6 7 14 1 6 7 13 8 9 14 5 3 10 11 1 2 0 4 12 14 8 9 1 2 0 12 10 7 13 3 4 5 11 6 4 5 3 12 10 11 9 14 0 1 6 7 13 8 2 8 9 14 2 0 1 10 11 13 6 4 5 3 12 7 2 0 1 5 3 4 13 6 14 8 12 10 11 7 9 11 12 10 6 7 13 2 0 5 3 14 8 9 1 4 7 13 6 9 14 8 3 4 11 12 2 0 1 5 10 9 14 8 0 1 2 11 12 6 7 5 3 4 10 13 n=16 ? n=17, a(17)=0 Announcement: -, Eduard I. Vatutin, before Aug 06 2023 Way of finding: cyclic DLS 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0 1 4 5 6 7 8 9 10 11 12 13 14 15 16 0 1 2 3 6 7 8 9 10 11 12 13 14 15 16 0 1 2 3 4 5 8 9 10 11 12 13 14 15 16 0 1 2 3 4 5 6 7 10 11 12 13 14 15 16 0 1 2 3 4 5 6 7 8 9 12 13 14 15 16 0 1 2 3 4 5 6 7 8 9 10 11 14 15 16 0 1 2 3 4 5 6 7 8 9 10 11 12 13 16 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0 1 2 5 6 7 8 9 10 11 12 13 14 15 16 0 1 2 3 4 7 8 9 10 11 12 13 14 15 16 0 1 2 3 4 5 6 9 10 11 12 13 14 15 16 0 1 2 3 4 5 6 7 8 11 12 13 14 15 16 0 1 2 3 4 5 6 7 8 9 10 13 14 15 16 0 1 2 3 4 5 6 7 8 9 10 11 12 15 16 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 n=18 ? n=19, a(19)=0 Announcement: -, Eduard I. Vatutin, before Aug 06 2023 Way of finding: cyclic DLS 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 0 1 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 0 1 2 3 6 7 8 9 10 11 12 13 14 15 16 17 18 0 1 2 3 4 5 8 9 10 11 12 13 14 15 16 17 18 0 1 2 3 4 5 6 7 10 11 12 13 14 15 16 17 18 0 1 2 3 4 5 6 7 8 9 12 13 14 15 16 17 18 0 1 2 3 4 5 6 7 8 9 10 11 14 15 16 17 18 0 1 2 3 4 5 6 7 8 9 10 11 12 13 16 17 18 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 18 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 0 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 0 1 2 5 6 7 8 9 10 11 12 13 14 15 16 17 18 0 1 2 3 4 7 8 9 10 11 12 13 14 15 16 17 18 0 1 2 3 4 5 6 9 10 11 12 13 14 15 16 17 18 0 1 2 3 4 5 6 7 8 11 12 13 14 15 16 17 18 0 1 2 3 4 5 6 7 8 9 10 13 14 15 16 17 18 0 1 2 3 4 5 6 7 8 9 10 11 12 15 16 17 18 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 17 18 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Aug 06 2023