A309210 - OEIS

%I #54 Jan 09 2024 11:03:13

%S 1,0,0,1,1,0,5,23,18865

%N Number of main classes of extended self-orthogonal diagonal Latin squares of order n.

%C A self-orthogonal diagonal Latin square (SODLS) is a diagonal Latin square orthogonal to its transpose. An extended self-orthogonal diagonal Latin square (ESODLS) is a diagonal Latin square that has an orthogonal diagonal Latin square from the same main class. SODLS is a special case of ESODLS.

%C A333366(n) <= A329685(n) <= a(n) <= A330391(n). - _Eduard I. Vatutin_, Jun 07 2020

%C a(10) >= 33240. - _Eduard I. Vatutin_, Jul 09 2020

%H E. I. Vatutin, <a href="https://vk.com/wall162891802_924">Discussion about properties of diagonal Latin squares</a> (in Russian)

%H E. I. Vatutin, <a href="https://vk.com/wall162891802_1134">About the lower bound of number of ESODLS of order 10</a> (in RUssian).

%H E. I. Vatutin, <a href="http://evatutin.narod.ru/evatutin_esodls_1_to_8.zip">List of all main classes of extended self-orthogonal diagonal Latin squares of orders 1-8</a>.

%H E. I. Vatutin, <a href="http://evatutin.narod.ru/evatutin_esodls_9.zip">List of all main classes of extended self-orthogonal diagonal Latin squares of order 9</a>.

%H E. Vatutin and A. Belyshev, <a href="https://www.springerprofessional.de/en/enumerating-the-orthogonal-diagonal-latin-squares-of-small-order/18659992">Enumerating the Orthogonal Diagonal Latin Squares of Small Order for Different Types of Orthogonality</a>, Communications in Computer and Information Science, Vol. 1331, Springer, 2020, pp. 586-597.

%H Eduard I. Vatutin, Natalia N. Nikitina, and Maxim O. Manzuk, <a href="https://vk.com/wall162891802_1485">First results of an experiment on studying the properties of DLS of order 9 in the volunteer distributed computing projects Gerasim@Home and RakeSearch</a> (in Russian).

%H Eduard Vatutin and Oleg Zaikin, <a href="https://doi.org/10.1007/978-3-031-49435-2_2">Classification of Cells Mapping Schemes Related to Orthogonal Diagonal Latin Squares of Small Order</a>, Supercomputing, Russian Supercomputing Days (RuSCDays 2023) Rev. Selected Papers Part II, LCNS Vol. 14389, Springer, Cham, 21-34.

%H <a href="/index/La#Latin">Index entries for sequences related to Latin squares and rectangles</a>

%e The diagonal Latin square

%e   0 1 2 3 4 5 6 7 8 9

%e   1 2 0 4 5 7 9 8 6 3

%e   5 0 1 6 3 9 8 2 4 7

%e   9 3 5 8 2 1 7 4 0 6

%e   4 6 3 5 7 8 0 9 2 1

%e   8 4 6 9 1 3 2 5 7 0

%e   7 8 9 0 6 4 5 1 3 2

%e   2 9 4 7 8 0 3 6 1 5

%e   6 5 7 1 0 2 4 3 9 8

%e   3 7 8 2 9 6 1 0 5 4

%e has the orthogonal diagonal Latin square

%e   0 1 2 3 4 5 6 7 8 9

%e   3 5 9 8 6 2 0 1 4 7

%e   4 3 8 7 2 1 9 0 5 6

%e   6 9 3 4 8 0 1 2 7 5

%e   7 2 0 1 9 3 5 8 6 4

%e   2 0 1 5 7 6 4 9 3 8

%e   8 6 4 2 0 9 7 5 1 3

%e   1 7 6 0 5 4 8 3 9 2

%e   9 8 5 6 1 7 3 4 2 0

%e   5 4 7 9 3 8 2 6 0 1

%e from the same main class.

%Y Cf. A287761, A333366, A329685, A330391.

%K nonn,more,hard

%O 1,7

%A _Eduard I. Vatutin_, Aug 09 2019

%E a(9) added by _Eduard I. Vatutin_, Dec 08 2020