Minimum 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)=16 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 1 2 3 0 5 7 4 6 5 4 6 7 0 1 3 2 4 6 7 5 3 0 2 1 7 5 4 6 1 2 0 3 6 7 5 4 2 3 1 0 3 0 1 2 6 4 7 5 2 3 0 1 7 6 5 4 n=10, a(10)<=25 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 1 6 5 2 9 0 7 4 3 8 3 2 9 5 1 8 4 0 7 6 5 9 6 1 2 7 8 3 0 4 6 7 0 4 8 1 5 9 2 3 4 0 3 8 7 2 1 6 9 5 9 8 7 6 5 4 3 2 1 0 8 3 4 7 0 9 2 5 6 1 7 5 8 0 3 6 9 1 4 2 2 4 1 9 6 3 0 8 5 7 n=12, a(12)<=36 Announcement: -, Eduard I. Vatutin, Feb 23 2024 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 7 10 11 8 6 9 9 6 8 11 10 7 5 4 3 2 1 0 4 0 1 5 3 2 10 6 7 11 9 8 11 8 9 10 7 6 4 3 5 1 0 2 8 9 6 7 11 10 1 5 4 0 2 3 10 7 11 9 6 8 3 0 2 5 4 1 6 10 7 8 9 11 2 1 0 3 5 4 2 5 3 0 1 4 8 11 9 6 7 10 7 11 10 6 8 9 0 2 1 4 3 5 3 4 5 2 0 1 9 8 6 10 11 7 5 3 4 1 2 0 11 9 10 7 8 6 n=14, a(14)<=49 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 6 11 0 5 12 10 9 4 3 1 8 13 2 7 1 7 9 0 8 11 3 10 2 5 13 4 6 12 9 3 6 2 0 12 5 8 1 13 11 7 10 4 12 6 4 13 5 2 10 3 11 8 0 9 7 1 10 8 12 4 11 7 0 13 6 2 9 1 5 3 7 2 13 8 1 3 4 9 10 12 5 0 11 6 13 12 11 10 9 8 7 6 5 4 3 2 1 0 4 10 7 11 13 1 8 5 12 0 2 6 3 9 2 9 8 6 10 13 12 1 0 3 7 5 4 11 8 13 3 12 6 4 2 11 9 7 1 10 0 5 11 4 5 7 3 0 1 12 13 10 6 8 9 2 5 0 10 1 7 9 11 2 4 6 12 3 13 8 3 5 1 9 2 6 13 0 7 11 4 12 8 10 n=16, a(16)<=64 Announcement: -, Eduard I. Vatutin, Dec 23 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 2 10 8 14 15 9 4 3 12 11 6 0 1 7 5 13 8 15 5 2 6 11 12 14 1 3 4 9 13 10 0 7 5 6 3 11 7 1 15 2 13 0 14 8 4 12 9 10 12 13 9 8 14 0 5 4 11 10 15 1 7 6 2 3 7 0 10 13 9 4 3 1 14 12 11 6 2 5 15 8 1 4 0 5 12 8 2 9 6 13 7 3 10 15 11 14 14 11 15 10 3 7 13 6 9 2 8 12 5 0 4 1 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 9 8 4 0 13 3 14 5 10 1 12 2 15 11 7 6 4 12 14 9 5 2 7 15 0 8 13 10 6 1 3 11 13 5 7 1 0 6 11 12 3 4 9 15 14 8 10 2 3 2 6 7 1 15 10 11 4 5 0 14 8 9 13 12 10 9 12 4 8 14 0 13 2 15 1 7 11 3 6 5 11 3 1 6 10 13 8 0 15 7 2 5 9 14 12 4 6 7 11 15 2 12 1 10 5 14 3 13 0 4 8 9 n=18, a(18)<=81 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 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 3 9 1 6 7 0 4 15 12 5 2 13 17 10 11 16 8 14 8 4 3 12 6 7 16 0 15 2 17 1 10 11 5 14 13 9 7 2 6 4 5 3 9 1 17 0 16 8 14 12 13 11 15 10 1 12 4 7 17 11 2 9 14 3 8 15 6 0 10 13 5 16 16 5 13 10 0 6 15 8 3 14 9 2 11 17 7 4 12 1 5 10 0 8 1 15 14 13 6 11 4 3 2 16 9 17 7 12 9 13 14 5 11 10 1 17 2 15 0 16 7 6 12 3 4 8 12 7 17 9 16 2 3 4 11 6 13 14 15 1 8 0 10 5 6 0 5 15 9 13 7 14 1 16 3 10 4 8 2 12 17 11 14 8 16 11 10 17 13 2 5 12 15 4 0 7 6 1 9 3 2 11 10 1 3 9 0 12 13 4 5 17 8 14 16 7 6 15 11 17 12 2 8 4 10 3 16 1 14 7 13 9 15 5 0 6 4 14 9 0 2 1 12 11 10 7 6 5 16 15 17 8 3 13 15 6 7 16 14 8 17 5 4 13 12 0 9 3 1 10 11 2 13 3 8 17 15 16 5 6 7 10 11 12 1 2 0 9 14 4 10 15 11 13 12 14 8 16 0 17 1 9 3 5 4 6 2 7 n=20, a(20)<=100 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 5 3 0 10 18 6 4 17 7 11 8 12 2 15 13 1 9 19 16 14 18 8 13 17 3 15 7 19 10 5 14 9 0 12 4 16 2 6 11 1 11 2 15 14 12 0 10 18 13 16 3 6 1 9 19 7 5 4 17 8 7 15 11 18 19 17 14 9 16 6 13 3 10 5 2 0 1 8 4 12 3 10 1 12 13 11 19 15 5 2 17 14 4 0 8 6 7 18 9 16 17 5 9 6 8 12 1 16 0 15 4 19 3 18 7 11 13 10 14 2 15 13 16 19 17 9 11 5 1 7 12 18 14 8 10 2 0 3 6 4 6 7 5 15 9 1 16 8 2 0 19 17 11 3 18 10 4 14 12 13 4 6 3 0 2 10 8 14 18 12 7 1 5 11 9 17 19 16 13 15 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 10 0 12 8 14 16 17 13 15 18 1 4 6 2 3 5 11 7 19 9 14 16 19 9 1 13 15 2 12 8 11 7 17 4 6 18 10 0 3 5 1 11 6 2 16 4 12 0 9 14 5 10 19 7 15 3 17 13 8 18 9 19 7 11 5 3 2 6 4 1 18 15 13 17 16 14 8 12 0 10 2 14 10 13 11 7 18 3 19 4 15 0 16 1 12 8 6 9 5 17 12 4 8 1 0 2 5 10 3 13 6 16 9 14 17 19 18 11 15 7 8 17 4 5 7 19 9 1 6 3 16 13 18 10 0 12 14 15 2 11 16 9 18 7 6 8 0 4 14 17 2 5 15 19 11 13 12 1 10 3 13 12 14 4 10 18 3 11 17 19 0 2 8 16 1 9 15 5 7 6 n=22, a(22)<=121 Announcement: -, Eduard I. Vatutin, Jan 22 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 20 21 3 13 6 9 5 1 14 17 21 11 2 19 10 0 4 7 20 16 12 15 8 18 19 11 8 7 20 6 16 21 12 4 3 18 17 9 0 5 15 1 14 13 10 2 9 16 7 19 15 17 18 8 10 20 0 21 1 11 13 3 4 6 2 14 5 12 18 8 15 12 16 20 7 4 0 10 19 2 11 21 17 14 1 5 9 6 13 3 1 21 3 15 8 12 11 16 17 2 14 7 19 4 5 10 9 13 6 18 0 20 6 17 20 10 0 3 9 19 14 8 5 16 13 7 2 12 18 21 11 1 4 15 16 15 11 4 19 13 0 3 1 14 12 9 7 20 18 21 8 2 17 10 6 5 13 19 5 0 14 11 17 9 6 3 1 20 18 15 12 4 10 7 21 16 2 8 7 9 21 8 3 2 20 10 5 15 17 4 6 16 11 1 19 18 13 0 12 14 20 0 18 6 13 9 10 5 4 19 7 14 2 17 16 11 12 8 15 3 21 1 8 2 16 21 7 10 4 12 15 18 20 1 3 6 9 17 11 14 0 5 19 13 17 7 12 20 11 0 19 6 3 16 8 13 5 18 15 2 21 10 1 9 14 4 15 4 1 11 21 18 12 2 7 13 16 5 8 14 19 9 3 0 10 20 17 6 2 10 13 14 1 15 5 0 9 17 18 3 4 12 21 16 6 20 7 8 11 19 14 12 0 13 18 19 1 11 16 6 4 17 15 5 10 20 2 3 8 21 9 7 12 5 14 2 6 4 3 13 11 1 21 0 20 10 8 18 17 15 19 7 16 9 4 14 9 1 10 21 2 15 18 5 13 8 16 3 6 19 0 11 20 12 7 17 5 6 10 17 2 8 21 18 20 7 9 12 14 1 3 0 13 19 4 11 15 16 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 10 3 4 5 12 7 8 1 2 21 15 6 0 19 20 13 14 9 16 17 18 11 11 18 17 16 9 14 13 20 19 0 6 15 21 2 1 8 7 12 5 4 3 10 n=24, a(24)<=144 Announcement: -, Eduard I. Vatutin, Feb 04 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 20 21 22 23 18 17 9 10 22 3 16 11 2 0 8 19 4 15 23 21 12 7 20 1 13 14 6 5 4 0 3 12 7 10 21 14 18 1 17 8 15 6 22 5 9 2 13 16 11 20 23 19 1 8 12 16 2 19 13 18 23 6 9 20 3 14 17 0 5 10 4 21 7 11 15 22 2 5 22 6 15 12 20 0 13 19 16 14 9 7 4 10 23 3 11 8 17 1 18 21 9 20 13 4 11 21 18 15 6 7 22 0 23 1 16 17 8 5 2 12 19 10 3 14 10 2 18 1 3 23 14 4 16 8 11 6 17 12 15 7 19 9 0 20 22 5 21 13 21 18 1 17 8 11 3 23 10 4 7 9 14 16 19 13 0 20 12 15 6 22 5 2 13 21 5 22 20 0 9 19 7 15 12 17 6 11 8 16 4 14 23 3 1 18 2 10 8 12 7 23 18 6 1 13 14 20 19 21 2 4 3 9 10 22 17 5 0 16 11 15 3 19 17 8 14 7 23 1 11 18 2 13 10 21 5 12 22 0 16 9 15 6 4 20 17 16 23 14 10 1 8 2 19 11 3 5 18 20 12 4 21 15 22 13 9 0 7 6 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 22 15 11 7 21 4 10 5 0 17 14 3 20 9 6 23 18 13 19 2 16 12 8 1 16 9 19 2 23 15 12 17 20 10 18 22 1 5 13 3 6 11 8 0 21 4 14 7 12 10 8 18 6 14 19 3 1 21 0 7 16 23 2 22 20 4 9 17 5 15 13 11 20 4 6 15 9 16 0 22 12 5 21 10 13 2 18 11 1 23 7 14 8 17 19 3 6 7 0 9 13 22 15 21 4 12 20 18 5 3 11 19 2 8 1 10 14 23 16 17 19 23 20 11 16 13 2 9 5 22 6 15 8 17 1 18 14 21 10 7 12 3 0 4 11 13 15 5 17 9 4 20 22 2 23 16 7 0 21 1 3 19 14 6 18 8 10 12 14 3 10 19 12 2 5 8 17 16 1 23 0 22 7 6 15 18 21 11 4 13 20 9 7 14 4 21 0 8 11 6 3 13 5 1 22 18 10 20 17 12 15 23 2 19 9 16 15 11 16 0 5 17 22 10 9 3 4 2 21 19 20 14 13 1 6 18 23 7 12 8 5 6 14 13 1 20 7 12 21 23 15 4 19 8 0 2 11 16 3 22 10 9 17 18 Dec 18 2024