Maximum number of intercalates in Brown's diagonal Latin squares of order N=2n, https://oeis.org/A382270 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 1 (a(10)>=57): -, Eduard I. Vatutin, Dec 18 2024 Way of finding 1: from experiments with intercalates spectra for LS/DLS Announcement 2 (a(10)=57): -, Oleg S. Zaikin, Eduard I. Vatutin, Mar 26 2025 Way of finding 2: SAT-based Brute Force 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 n=26, a(26)>=497 Announcement: -, Eduard I. Vatutin, Feb 17 2025 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 24 25 12 15 0 24 11 17 5 4 6 22 23 16 7 18 9 2 3 19 21 20 8 14 1 25 10 13 22 13 6 8 23 15 18 11 0 4 24 5 9 16 20 1 21 25 14 7 10 2 17 19 12 3 11 17 4 23 12 1 15 3 16 5 19 18 0 25 7 6 20 9 22 10 24 13 2 21 8 14 4 2 16 10 7 3 1 12 5 6 14 0 8 17 25 11 19 20 13 24 22 18 15 9 23 21 17 14 20 6 9 2 12 1 21 18 25 15 22 3 10 0 7 4 24 13 23 16 19 5 11 8 9 19 17 18 25 14 4 5 10 23 22 12 24 1 13 3 2 15 20 21 11 0 7 8 6 16 16 6 8 7 0 11 21 20 15 2 3 13 1 24 12 22 23 10 5 4 14 25 18 17 19 9 23 22 24 4 17 12 9 10 11 25 18 6 20 5 19 7 0 14 15 16 13 8 21 1 3 2 21 23 9 15 18 22 24 13 20 19 11 25 17 8 0 14 6 5 12 1 3 7 10 16 2 4 3 12 19 17 2 10 7 14 25 21 1 20 16 9 5 24 4 0 11 18 15 23 8 6 13 22 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 14 8 21 2 13 24 10 22 9 20 6 7 25 0 18 19 5 16 3 15 1 12 23 4 17 11 8 11 5 19 16 23 13 24 4 7 0 10 3 22 15 25 18 21 1 12 2 9 6 20 14 17 13 10 25 1 14 8 20 21 19 3 2 9 18 7 16 23 22 6 4 5 17 11 24 0 15 12 20 7 12 25 19 21 3 16 2 15 17 1 11 14 24 8 10 23 9 22 4 6 0 13 18 5 6 21 14 5 22 7 0 17 1 13 16 23 10 15 2 9 12 24 8 25 18 3 20 11 4 19 10 25 18 11 5 9 17 6 12 1 21 22 2 23 3 4 24 13 19 8 16 20 14 7 0 15 2 3 1 21 8 13 16 15 14 0 7 19 5 20 6 18 25 11 10 9 12 17 4 24 22 23 15 0 7 14 20 16 8 19 13 24 4 3 23 2 22 21 1 12 6 17 9 5 11 18 25 10 5 18 13 0 6 4 22 9 23 10 8 24 14 11 1 17 15 2 16 3 21 19 25 12 7 20 18 5 10 16 1 19 2 25 22 14 12 17 4 21 8 13 11 3 0 23 6 24 9 15 20 7 19 4 11 20 3 18 25 8 24 12 9 2 15 10 23 16 13 1 17 0 7 22 5 14 21 6 24 9 22 12 10 25 11 23 18 8 5 4 6 19 21 20 17 7 2 14 0 15 13 3 16 1 1 16 3 13 15 0 14 2 7 17 20 21 19 6 4 5 8 18 23 11 25 10 12 22 9 24 7 20 15 9 24 6 23 0 3 11 13 8 21 4 17 12 14 22 25 2 19 1 16 10 5 18 n=28, a(28)>=524 Announcement: -, Eduard I. Vatutin, Feb 17 2025 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 24 25 26 27 17 2 20 13 27 12 16 8 9 26 6 4 22 3 24 5 23 21 1 18 19 11 15 0 14 7 25 10 4 22 10 6 14 8 26 9 3 11 2 7 0 12 15 27 20 25 16 24 18 1 19 13 21 17 5 23 5 11 0 8 3 4 15 17 6 20 14 1 2 18 9 25 26 13 7 21 10 12 23 24 19 27 16 22 23 5 17 21 13 19 1 18 24 16 25 20 27 15 12 0 7 2 11 3 9 26 8 14 6 10 22 4 6 15 4 11 19 18 13 3 25 5 1 27 20 17 10 7 0 26 22 2 24 14 9 8 16 23 12 21 12 6 5 18 17 11 3 23 27 13 7 25 19 26 1 8 2 20 14 0 4 24 16 10 9 22 21 15 24 14 12 22 11 1 4 21 7 2 19 17 18 27 0 9 10 8 25 20 6 23 26 16 5 15 13 3 25 10 13 7 12 0 9 26 5 8 24 21 4 16 11 23 6 3 19 22 1 18 27 15 20 14 17 2 21 12 23 16 8 9 14 24 2 22 26 0 7 10 17 20 27 1 5 25 3 13 18 19 11 4 15 6 26 8 3 15 7 2 10 27 13 6 23 9 11 5 22 16 18 4 21 14 0 17 25 20 12 24 19 1 22 16 27 19 24 23 12 10 21 7 13 26 25 9 18 2 1 14 20 6 17 15 4 3 8 0 11 5 8 27 18 25 26 21 22 14 23 3 11 15 17 20 7 10 12 16 24 4 13 5 6 1 2 9 0 19 11 24 6 10 9 20 19 22 15 4 0 13 26 25 2 1 14 27 23 12 5 8 7 18 17 21 3 16 3 13 15 5 16 26 23 6 20 25 8 10 9 0 27 18 17 19 2 7 21 4 1 11 22 12 14 24 18 7 19 26 21 10 0 25 11 15 22 3 13 4 23 14 24 5 12 16 2 27 17 6 1 8 20 9 19 0 9 2 1 6 5 13 4 24 16 12 10 7 20 17 15 11 3 23 14 22 21 26 25 18 27 8 14 23 11 27 2 3 7 12 1 10 18 5 21 19 8 6 22 9 17 26 15 20 24 25 0 16 4 13 1 19 24 12 20 25 17 0 14 21 4 18 16 22 5 11 9 23 6 13 27 10 2 7 15 3 8 26 13 4 16 0 25 24 20 15 26 17 9 22 6 8 19 21 5 18 10 1 12 7 3 2 27 11 23 14 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 10 25 7 14 0 15 11 19 18 1 21 23 5 24 3 22 4 6 26 9 8 16 12 27 13 20 2 17 15 21 22 9 10 16 24 4 0 14 20 2 8 1 26 19 25 7 13 27 23 3 11 17 18 5 6 12 2 17 14 20 15 27 18 1 22 19 3 6 23 11 16 4 21 24 8 5 26 9 0 12 7 13 10 25 20 9 26 23 22 13 2 11 17 0 15 19 24 21 6 3 8 12 27 10 16 25 14 5 4 1 18 7 9 20 8 1 6 17 27 2 16 12 5 24 14 23 4 13 3 22 15 11 25 0 10 21 26 19 7 18 16 3 21 17 18 7 8 5 12 23 27 14 1 2 25 26 13 0 4 15 22 19 20 9 10 6 24 11 7 18 1 4 5 14 25 16 10 27 12 8 3 6 21 24 19 15 0 17 11 2 13 22 23 26 9 20 Mar 26 2025