Maximal size of main class for diagonal Latin squares of order n with first row 1..n, https://oeis.org/A299784 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)=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 Way of finding: brute force 0 1 2 3 4 5 1 2 0 5 3 4 4 3 5 0 2 1 3 0 1 4 5 2 5 4 3 2 1 0 2 5 4 1 0 3 n=7, a(7)=192 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 4 6 0 3 5 0 3 6 2 4 1 2 4 6 1 0 3 5 6 3 4 0 5 1 2 4 5 1 2 3 6 0 3 6 0 5 1 2 4 n=8, a(8)=1536 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 7 1 2 5 6 7 3 0 4 5 7 1 0 6 2 4 3 7 3 6 4 1 0 5 2 2 6 4 5 3 7 1 0 4 5 3 7 0 6 2 1 3 4 0 2 5 1 7 6 6 0 7 1 2 4 3 5 n=9, a(9)=1536 Announcement: https://vk.com/wall162891802_1103, Eduard I. Vatutin, Mar 14 2020 Way of finding: equal to the theoretical maximum from combinations of M-transformations 0 1 2 3 4 5 6 7 8 1 2 4 6 5 7 8 0 3 8 5 3 7 0 6 1 2 4 5 7 0 8 1 2 3 4 6 2 3 5 4 6 0 7 8 1 7 8 1 5 3 4 0 6 2 4 6 7 2 8 1 5 3 0 6 4 8 0 7 3 2 1 5 3 0 6 1 2 8 4 5 7 n=10, a(10)=15360 Announcement: https://vk.com/wall162891802_1103, Eduard I. Vatutin, Mar 14 2020 Way of finding: equal to the theoretical maximum from combinations of M-transformations 0 1 2 3 4 5 6 7 8 9 1 2 0 4 5 3 9 8 6 7 3 5 6 1 8 7 4 0 9 2 9 4 7 8 3 2 1 6 0 5 2 7 3 0 9 8 5 1 4 6 6 8 5 9 2 4 7 3 1 0 4 6 9 7 0 1 3 2 5 8 7 0 4 6 1 9 8 5 2 3 8 3 1 5 6 0 2 9 7 4 5 9 8 2 7 6 0 4 3 1 n=11, a(11)=15360 Announcement: https://vk.com/wall162891802_1106, Eduard I. Vatutin, Mar 22 2020 Way of finding: equal to the theoretical maximum from combinations of M-transformations 0 1 2 3 4 5 6 7 8 9 10 9 2 8 1 5 10 3 4 6 0 7 3 10 1 6 0 4 7 9 2 5 8 2 0 9 4 8 7 10 1 5 6 3 1 6 5 7 3 2 4 10 9 8 0 5 8 4 10 1 6 9 0 3 7 2 10 3 6 8 7 9 5 2 0 1 4 7 4 0 5 9 1 2 8 10 3 6 4 5 3 9 10 0 8 6 7 2 1 6 9 7 0 2 8 1 3 4 10 5 8 7 10 2 6 3 0 5 1 4 9 n=12, a(12)=184320 Announcement: https://vk.com/wall162891802_1106, Eduard I. Vatutin, Mar 22 2020 Way of finding: equal to the theoretical maximum from combinations of M-transformations 0 1 2 3 4 5 6 7 8 9 10 11 9 2 10 1 6 4 11 3 5 7 0 8 7 10 1 9 0 3 4 11 6 2 8 5 11 7 3 4 9 10 2 0 1 8 5 6 5 6 7 10 3 8 9 4 0 11 1 2 1 5 0 11 8 6 3 2 9 4 7 10 2 8 4 0 11 7 5 6 10 3 9 1 3 0 9 2 5 1 10 8 11 6 4 7 8 3 5 6 10 11 1 9 7 0 2 4 6 11 8 5 2 9 7 1 4 10 3 0 4 9 6 7 1 0 8 10 2 5 11 3 10 4 11 8 7 2 0 5 3 1 6 9 n=13, a(13)=184320 Announcement: https://vk.com/wall162891802_1106, Eduard I. Vatutin, Mar 22 2020 Way of finding: equal to the theoretical maximum from combinations of M-transformations 0 1 2 3 4 5 6 7 8 9 10 11 12 10 2 11 1 5 3 12 4 6 7 8 0 9 8 10 1 11 0 4 3 12 5 6 2 9 7 12 5 3 4 8 11 7 9 0 1 6 2 10 6 8 9 7 3 12 11 10 4 0 1 5 2 2 0 7 10 11 6 9 3 12 4 5 8 1 4 6 8 2 12 9 5 11 1 3 7 10 0 1 12 0 6 10 7 2 8 9 5 11 3 4 3 9 4 12 6 10 8 2 7 11 0 1 5 5 4 6 8 9 2 0 1 11 10 12 7 3 11 3 10 0 7 1 4 5 2 12 9 6 8 7 11 5 9 1 8 10 0 3 2 4 12 6 9 7 12 5 2 0 1 6 10 8 3 4 11 n=14, a(14)=2580480 Announcement: https://vk.com/wall162891802_1106, Eduard I. Vatutin, Mar 22 2020 Way of finding: equal to the theoretical maximum from combinations of M-transformations 0 1 2 3 4 5 6 7 8 9 10 11 12 13 11 2 12 1 6 3 8 13 4 5 7 9 0 10 8 10 1 12 0 4 3 5 13 11 6 2 9 7 5 12 11 4 13 7 0 2 10 3 1 6 8 9 6 8 10 13 3 12 9 0 5 4 2 7 11 1 7 4 13 9 12 6 10 11 3 2 0 8 1 5 13 3 7 2 11 9 5 6 0 12 4 1 10 8 9 6 3 0 2 13 7 8 11 1 12 10 5 4 10 9 6 5 1 8 13 12 7 0 11 3 4 2 3 13 4 11 5 1 12 9 2 10 8 0 7 6 2 0 5 10 7 11 4 1 6 8 9 13 3 12 4 5 9 7 8 10 11 3 1 6 13 12 2 0 1 11 8 6 9 0 2 10 12 7 5 4 13 3 12 7 0 8 10 2 1 4 9 13 3 5 6 11 n=15, a(15)=2580480 Announcement: https://vk.com/wall162891802_1106, Eduard I. Vatutin, Mar 22 2020 Way of finding: equal to the theoretical maximum from combinations of M-transformations 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 12 2 11 1 6 3 7 13 14 4 5 8 9 0 10 9 11 1 12 0 4 3 6 5 13 14 7 2 10 8 3 10 13 4 11 8 0 9 2 5 12 1 14 6 7 1 9 14 7 3 13 11 5 0 12 4 6 10 8 2 14 12 10 5 13 6 2 4 11 3 0 9 8 7 1 10 4 7 8 14 12 5 11 6 0 2 13 1 9 3 6 0 3 2 7 9 14 8 12 1 11 10 13 4 5 8 3 0 11 10 14 9 1 7 2 13 4 5 12 6 2 6 4 13 8 7 12 3 9 10 1 14 0 5 11 7 8 6 0 5 11 10 12 13 14 9 2 3 1 4 13 7 5 10 2 0 8 14 1 6 3 12 4 11 9 4 14 12 6 9 1 13 10 3 8 7 5 11 2 0 5 13 8 9 1 2 4 0 10 11 6 3 7 14 12 11 5 9 14 12 10 1 2 4 7 8 0 6 3 13 Mar 11 2021