Maximum number of intercalates in Brown's diagonal Latin squares of order N=2n, https://oeis.org/Axxxxxx n=2, a(2)=0 Announcement: https://vk.com/wall162891802_2895, Eduard I. Vatutin, Dec 16 2024 - n=4, a(4)=12 Announcement: https://vk.com/wall162891802_2895, Eduard I. Vatutin, Dec 16 2024 Way of finding: brute force 0 1 2 3 2 3 0 1 3 2 1 0 1 0 3 2 n=6, a(6)=9 Announcement: https://vk.com/wall162891802_2895, Eduard I. Vatutin, Dec 16 2024 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=8, a(8)=112 Announcement: https://vk.com/wall162891802_2895, Eduard I. Vatutin, Dec 16 2024 Way of finding: brute force 0 1 2 3 4 5 6 7 2 3 0 1 6 7 4 5 4 5 6 7 0 1 2 3 6 7 4 5 2 3 0 1 3 2 1 0 7 6 5 4 1 0 3 2 5 4 7 6 7 6 5 4 3 2 1 0 5 4 7 6 1 0 3 2 n=10, a(10)>=57 Announcement: -, Eduard I. Vatutin, Dec 18 2024 Way of finding: from experiments with intercalates spectra for LS/DLS 0 1 2 3 4 5 6 7 8 9 3 7 8 5 0 9 4 1 2 6 6 2 1 4 9 0 5 8 7 3 4 6 9 8 2 7 1 0 3 5 9 8 7 6 5 4 3 2 1 0 8 9 4 2 6 3 7 5 0 1 2 5 6 0 8 1 9 3 4 7 1 0 5 7 3 6 2 4 9 8 5 3 0 1 7 2 8 9 6 4 7 4 3 9 1 8 0 6 5 2 n=12, a(12)>=252 Announcement: https://vk.com/wall162891802_1712, Eduard I. Vatutin, Jul 28 2021 Way of finding: from spectum of number of intercalates in DLS 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=14, a(14)>=385 Announcement: -, Eduard I. Vatutin, Feb 27 2024 Way of finding: from spectum of number of intercalates in DLS 0 1 2 3 4 5 6 7 8 9 10 11 12 13 1 4 6 5 12 3 2 8 7 13 0 10 11 9 2 6 13 7 9 11 1 0 10 4 8 5 3 12 4 12 9 8 11 7 13 5 3 2 1 0 10 6 8 7 10 4 3 12 0 1 5 6 2 13 9 11 6 2 1 11 13 9 8 10 0 12 7 3 5 4 7 8 0 12 5 4 10 3 1 11 6 9 13 2 13 9 12 0 6 10 4 2 11 1 5 8 7 3 5 3 11 1 7 8 9 4 12 0 13 2 6 10 9 13 4 10 2 0 12 11 6 5 3 7 8 1 10 0 8 9 1 13 7 6 2 3 11 12 4 5 3 5 7 13 8 1 11 12 4 10 9 6 2 0 11 10 5 6 0 2 3 9 13 7 12 4 1 8 12 11 3 2 10 6 5 13 9 8 4 1 0 7 n=16, a(16)>=960 Announcement: -, Eduard I. Vatutin, Dec 30 2023 Way of finding: from spectum of number of intercalates in DLS 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 2 3 0 1 5 4 7 6 9 8 11 10 14 15 12 13 3 2 1 0 6 7 4 5 10 11 8 9 15 14 13 12 1 0 3 2 7 6 5 4 11 10 9 8 13 12 15 14 8 11 9 10 14 12 13 15 0 2 3 1 5 6 4 7 10 9 11 8 13 15 14 12 3 1 0 2 7 4 6 5 11 8 10 9 15 13 12 14 1 3 2 0 6 5 7 4 9 10 8 11 12 14 15 13 2 0 1 3 4 7 5 6 14 15 12 13 8 9 10 11 4 5 6 7 2 3 0 1 13 12 15 14 10 11 8 9 6 7 4 5 1 0 3 2 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 12 13 14 15 9 8 11 10 5 4 7 6 0 1 2 3 6 5 7 4 3 1 0 2 13 15 14 12 11 8 10 9 7 4 6 5 1 3 2 0 15 13 12 14 10 9 11 8 4 7 5 6 0 2 3 1 14 12 13 15 9 10 8 11 5 6 4 7 2 0 1 3 12 14 15 13 8 11 9 10 n=18, a(18)>=329 Announcement: -, Eduard I. Vatutin, Aug 06 2023 Way of finding: from experiments with intercalates spectra for LS/DLS 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 5 7 17 8 15 4 14 1 11 6 16 3 13 2 9 0 10 12 14 0 8 7 12 16 15 6 4 13 11 2 1 5 10 9 17 3 8 5 14 16 7 11 17 4 15 2 13 0 6 10 1 3 12 9 9 12 3 1 10 6 0 13 2 15 4 17 11 7 16 14 5 8 16 2 7 5 6 14 4 9 0 17 8 13 3 11 12 10 15 1 3 17 9 10 5 1 2 11 13 4 6 15 16 12 7 8 0 14 13 14 5 6 9 2 1 17 7 10 0 16 15 8 11 12 3 4 15 6 13 17 1 7 9 5 3 14 12 8 10 16 0 4 11 2 12 10 0 9 2 13 3 16 6 11 1 14 4 15 8 17 7 5 7 9 6 13 14 17 12 2 16 1 15 5 0 3 4 11 8 10 10 8 11 4 3 0 5 15 1 16 2 12 17 14 13 6 9 7 11 13 1 2 0 8 10 3 5 12 14 7 9 17 15 16 4 6 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 1 15 10 12 11 3 13 8 17 0 9 4 14 6 5 7 2 16 6 4 16 15 17 9 7 14 12 5 3 10 8 0 2 1 13 11 2 11 4 0 16 10 8 12 14 3 5 9 7 1 17 13 6 15 4 3 12 11 8 15 16 0 10 7 17 1 2 9 6 5 14 13 n=20, a(20)>=356 Announcement: -, Eduard I. Vatutin, Jan 15 2024 Way of finding: from experiments with intercalates spectra for LS/DLS 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 4 6 12 2 1 8 3 19 9 14 5 10 0 16 11 18 17 7 13 15 5 2 11 9 3 7 1 4 19 6 13 0 15 18 12 16 10 8 17 14 8 7 4 1 2 6 9 3 5 0 19 14 16 10 13 17 18 15 12 11 1 0 10 7 13 17 5 11 4 16 3 15 8 14 2 6 12 9 19 18 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 13 3 14 15 0 18 8 10 2 12 7 17 9 11 1 19 4 5 16 6 6 16 5 4 19 1 11 9 17 7 12 2 10 8 18 0 15 14 3 13 18 19 9 12 6 2 14 8 15 3 16 4 11 5 17 13 7 10 0 1 11 12 15 18 17 13 10 16 14 19 0 5 3 9 6 2 1 4 7 8 16 11 18 19 14 10 15 6 12 2 17 7 13 4 9 5 0 1 8 3 3 8 1 0 5 9 4 13 7 17 2 12 6 15 10 14 19 18 11 16 12 5 13 11 10 19 17 1 16 4 15 3 18 2 0 9 8 6 14 7 15 13 7 17 18 11 16 0 10 5 14 9 19 3 8 1 2 12 6 4 14 17 8 10 16 12 18 15 0 13 6 19 4 1 7 3 9 11 2 5 7 14 6 8 9 0 2 18 3 15 4 16 1 17 19 10 11 13 5 12 10 4 19 14 8 16 12 2 13 1 18 6 17 7 3 11 5 0 15 9 2 10 3 13 7 15 0 14 18 8 11 1 5 19 4 12 6 16 9 17 9 15 0 5 11 3 7 17 6 18 1 13 2 12 16 8 14 19 4 10 17 9 16 6 12 4 19 5 1 11 8 18 14 0 15 7 13 3 10 2 n=22, a(22)>=497 Announcement: -, Eduard I. Vatutin, Mar 11 2024 Way of finding: from spectum of number of intercalates in DLS 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 3 5 13 9 6 0 14 10 19 4 20 1 17 2 11 7 21 15 12 8 16 18 1 6 9 13 18 10 21 4 7 2 5 16 19 14 17 0 11 3 8 12 15 20 10 9 6 14 2 1 3 5 0 13 4 17 8 21 16 18 20 19 7 15 12 11 18 16 8 12 15 21 7 11 2 17 1 20 4 19 10 14 0 6 9 13 5 3 11 12 15 7 19 20 18 16 21 8 17 4 13 0 5 3 1 2 14 6 9 10 2 3 5 17 0 7 1 8 15 10 9 12 11 6 13 20 14 21 4 16 18 19 4 13 7 10 12 3 5 2 20 15 21 0 6 1 19 16 18 9 11 14 8 17 14 2 17 5 20 15 12 21 11 3 13 8 18 10 0 9 6 1 16 4 19 7 15 17 11 21 8 12 19 20 3 16 14 7 5 18 1 2 9 13 0 10 4 6 19 18 16 4 21 14 20 13 6 11 12 9 10 15 8 1 7 0 17 5 3 2 9 10 1 15 7 4 8 18 16 0 2 19 21 5 3 13 17 14 6 20 11 12 8 21 18 20 5 19 10 12 17 14 6 15 7 4 9 11 2 16 1 3 0 13 6 4 10 0 13 9 2 1 18 5 7 14 16 3 20 19 12 8 21 11 17 15 12 11 20 6 14 17 13 3 5 21 19 2 0 16 18 8 4 7 15 1 10 9 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 5 7 0 2 10 13 17 6 12 1 18 3 20 9 15 4 8 11 19 21 14 16 16 14 21 19 11 8 4 15 9 20 3 18 1 12 6 17 13 10 2 0 7 5 20 15 12 8 3 11 0 17 14 19 16 5 2 7 4 21 10 18 13 9 6 1 7 19 4 16 1 6 9 0 10 18 8 13 3 11 21 12 15 20 5 17 2 14 13 0 3 1 16 2 11 9 4 7 15 6 14 17 12 10 19 5 20 18 21 8 17 8 14 11 9 18 16 19 1 6 0 21 15 20 2 5 3 12 10 7 13 4 n=24, a(24)>=1008 Announcement: -, Eduard I. Vatutin, Feb 20 2024 Way of finding: from spectum of number of intercalates in DLS 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 4 2 5 0 3 1 10 8 11 6 9 7 16 14 17 12 15 13 22 20 23 18 21 19 3 5 1 2 0 4 9 11 7 8 6 10 15 17 13 14 12 16 21 23 19 20 18 22 5 3 0 4 1 2 11 9 6 10 7 8 17 15 12 16 13 14 23 21 18 22 19 20 2 4 3 1 5 0 8 10 9 7 11 6 14 16 15 13 17 12 20 22 21 19 23 18 1 0 4 5 2 3 7 6 10 11 8 9 13 12 16 17 14 15 19 18 22 23 20 21 18 19 20 21 22 23 12 13 14 15 16 17 6 7 8 9 10 11 0 1 2 3 4 5 22 20 23 18 21 19 16 14 17 12 15 13 10 8 11 6 9 7 4 2 5 0 3 1 21 23 19 20 18 22 15 17 13 14 12 16 9 11 7 8 6 10 3 5 1 2 0 4 23 21 18 22 19 20 17 15 12 16 13 14 11 9 6 10 7 8 5 3 0 4 1 2 20 22 21 19 23 18 14 16 15 13 17 12 8 10 9 7 11 6 2 4 3 1 5 0 19 18 22 23 20 21 13 12 16 17 14 15 7 6 10 11 8 9 1 0 4 5 2 3 6 7 8 9 10 11 0 1 2 3 4 5 18 19 20 21 22 23 12 13 14 15 16 17 10 8 11 6 9 7 4 2 5 0 3 1 22 20 23 18 21 19 16 14 17 12 15 13 9 11 7 8 6 10 3 5 1 2 0 4 21 23 19 20 18 22 15 17 13 14 12 16 11 9 6 10 7 8 5 3 0 4 1 2 23 21 18 22 19 20 17 15 12 16 13 14 8 10 9 7 11 6 2 4 3 1 5 0 20 22 21 19 23 18 14 16 15 13 17 12 7 6 10 11 8 9 1 0 4 5 2 3 19 18 22 23 20 21 13 12 16 17 14 15 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5 6 7 8 9 10 11 16 14 17 12 15 13 22 20 23 18 21 19 4 2 5 0 3 1 10 8 11 6 9 7 15 17 13 14 12 16 21 23 19 20 18 22 3 5 1 2 0 4 9 11 7 8 6 10 17 15 12 16 13 14 23 21 18 22 19 20 5 3 0 4 1 2 11 9 6 10 7 8 14 16 15 13 17 12 20 22 21 19 23 18 2 4 3 1 5 0 8 10 9 7 11 6 13 12 16 17 14 15 19 18 22 23 20 21 1 0 4 5 2 3 7 6 10 11 8 9 Dec 18 2024