Minimal size of main class for diagonal Latin squares of order n with the first row in order, https://oeis.org/A299783 n=1, a(1)=1 Article: E. Vatutin, A. Belyshev, S. Kochemazov, O. Zaikin, N. Nikitina, Enumeration of isotopy classes of diagonal Latin squares of small order using volunteer computing, Communications in Computer and Information Science. Vol. 965. Springer, 2018. pp. 578-586. https://doi.org/10.1007/978-3-030-05807-4_49 Way of finding: brute force 0 n=2, a(2)=0 - n=3, a(3)=0 - n=4, a(4)=2 Article: E. Vatutin, A. Belyshev, S. Kochemazov, O. Zaikin, N. Nikitina, Enumeration of isotopy classes of diagonal Latin squares of small order using volunteer computing, Communications in Computer and Information Science. Vol. 965. Springer, 2018. pp. 578-586. https://doi.org/10.1007/978-3-030-05807-4_49 Way of finding: brute force 0 1 2 3 2 3 0 1 3 2 1 0 1 0 3 2 n=5, a(5)=4 Article: E. Vatutin, A. Belyshev, S. Kochemazov, O. Zaikin, N. Nikitina, Enumeration of isotopy classes of diagonal Latin squares of small order using volunteer computing, Communications in Computer and Information Science. Vol. 965. Springer, 2018. pp. 578-586. https://doi.org/10.1007/978-3-030-05807-4_49 Way of finding: brute force 0 1 2 3 4 2 3 4 0 1 4 0 1 2 3 1 2 3 4 0 3 4 0 1 2 n=6, a(6)=32 Article: E. Vatutin, A. Belyshev, S. Kochemazov, O. Zaikin, N. Nikitina, Enumeration of isotopy classes of diagonal Latin squares of small order using volunteer computing, Communications in Computer and Information Science. Vol. 965. Springer, 2018. pp. 578-586. https://doi.org/10.1007/978-3-030-05807-4_49 Way of finding: brute force 0 1 2 3 4 5 1 2 0 5 3 4 4 3 5 0 2 1 3 5 1 4 0 2 5 4 3 2 1 0 2 0 4 1 5 3 n=7, a(7)=32 Article: E. Vatutin, A. Belyshev, S. Kochemazov, O. Zaikin, N. Nikitina, Enumeration of isotopy classes of diagonal Latin squares of small order using volunteer computing, Communications in Computer and Information Science. Vol. 965. Springer, 2018. pp. 578-586. https://doi.org/10.1007/978-3-030-05807-4_49 Way of finding: brute force 0 1 2 3 4 5 6 1 2 5 6 0 3 4 4 6 3 0 5 1 2 5 4 6 1 3 2 0 3 5 4 2 6 0 1 6 0 1 5 2 4 3 2 3 0 4 1 6 5 n=8, a(8)=96 Article: E. Vatutin, A. Belyshev, S. Kochemazov, O. Zaikin, N. Nikitina, Enumeration of isotopy classes of diagonal Latin squares of small order using volunteer computing, Communications in Computer and Information Science. Vol. 965. Springer, 2018. pp. 578-586. https://doi.org/10.1007/978-3-030-05807-4_49 0 1 2 3 4 5 6 7 1 2 3 5 7 6 0 4 3 0 1 7 5 4 2 6 5 6 7 4 3 0 1 2 7 3 5 1 6 2 4 0 4 7 6 0 2 3 5 1 6 5 4 2 0 1 7 3 2 4 0 6 1 7 3 5 n=9, a(9)<=48 Announcement: https://vk.com/wall162891802_1234, Eduard I. Vatutin, Jun 09 2020 Way of finding: one of known orthogonal diagonal Latin squares 0 1 2 3 4 5 6 7 8 2 4 3 0 7 6 8 1 5 6 2 8 5 3 4 7 0 1 4 6 7 1 8 2 3 5 0 1 5 4 7 6 0 2 8 3 7 8 1 4 5 3 0 6 2 3 7 0 2 1 8 5 4 6 8 3 5 6 0 7 1 2 4 5 0 6 8 2 1 4 3 7 n=10, a(10)<=7680 Announcement: https://vk.com/wall162891802_1233, Eduard I. Vatutin, Jun 09 2020 Way of finding: one of known orthogonal diagonal Latin squares 0 1 2 3 4 5 6 7 8 9 1 2 0 4 3 6 5 9 7 8 2 0 3 5 8 1 4 6 9 7 4 6 9 7 1 8 2 0 3 5 9 7 8 6 5 4 3 1 2 0 3 4 7 8 0 9 1 2 5 6 6 9 4 1 7 2 8 5 0 3 7 8 5 0 6 3 9 4 1 2 5 3 1 9 2 7 0 8 6 4 8 5 6 2 9 0 7 3 4 1 n=11, a(11)<=1536 Announcement: https://vk.com/wall162891802_1577, Eduard I. Vatutin, Mar 16 2021 Way of finding: cyclic diagonal Latin squares 0 1 2 3 4 5 6 7 8 9 10 1 2 3 5 6 9 7 10 0 4 8 7 10 8 0 3 1 5 9 6 2 4 3 5 9 4 10 6 8 0 2 7 1 4 6 7 10 1 8 2 3 9 0 5 5 9 4 6 8 7 0 1 3 10 2 10 8 0 1 5 2 9 4 7 3 6 6 7 10 8 2 0 3 5 4 1 9 8 0 1 2 9 3 4 6 10 5 7 2 3 5 9 7 4 10 8 1 6 0 9 4 6 7 0 10 1 2 5 8 3 n=12, a(12)<=46080 Announcement: https://vk.com/wall162891802_1631, Eduard I. Vatutin, Apr 04 2021 Way of finding: search in the neighborhood of central symmetry 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 9 0 7 1 10 4 11 2 6 8 2 10 6 8 11 4 7 0 3 5 1 9 9 6 1 11 3 7 4 8 0 10 5 2 8 4 5 2 0 10 1 11 9 6 7 3 5 9 8 7 10 0 11 1 4 3 2 6 4 3 11 1 6 2 9 5 10 0 8 7 7 0 3 5 1 9 2 10 6 8 11 4 6 8 4 10 2 11 0 9 1 7 3 5 11 7 10 9 8 6 5 3 2 1 4 0 10 11 7 6 9 8 3 2 5 4 0 1 n=13, a(13)<=7680 Announcement: https://vk.com/wall162891802_1578, Eduard I. Vatutin, Mar 16 2021 Way of finding: cyclic diagonal Latin squares 0 1 2 3 4 5 6 7 8 9 10 11 12 2 3 4 6 5 7 9 8 10 11 12 0 1 8 0 10 2 12 1 4 3 6 5 9 7 11 10 2 12 4 1 3 5 6 9 7 11 8 0 6 8 9 10 11 0 12 2 4 1 5 3 7 4 6 5 9 7 8 11 10 12 0 1 2 3 9 10 11 12 0 2 1 4 5 3 7 6 8 12 4 1 5 3 6 7 9 11 8 0 10 2 11 12 0 1 2 4 3 5 7 6 8 9 10 5 9 7 11 8 10 0 12 1 2 3 4 6 7 11 8 0 10 12 2 1 3 4 6 5 9 1 5 3 7 6 9 8 11 0 10 2 12 4 3 7 6 8 9 11 10 0 2 12 4 1 5 Apr 04 2021