cp's OEIS Frontend

A333367 Number of doubly self-orthogonal diagonal Latin squares of order n with the first row in ascending order.

%I A333367 #40 Oct 06 2023 16:09:31
%S A333367 1,0,0,2,4,0,64,1152,28608,0
%N A333367 Number of doubly self-orthogonal diagonal Latin squares of order n with the first row in ascending order.
%C A333367 A doubly self-orthogonal diagonal Latin square (DSODLS) is a diagonal Latin square orthogonal to its transpose and antitranspose.
%C A333367 a(n) <= A287761(n) <= A309598(n) <= A305570(n). - _Eduard I. Vatutin_, Jun 06 2020
%H A333367 R. Lu, S. Liu, and J. Zhang, <a href="https://doi.org/10.1007/978-3-642-23786-7_41">Searching for Doubly Self-orthogonal Latin Squares</a>. Lecture Notes in Computer Science 6876 (2011), 538-545.
%H A333367 E. I. Vatutin, <a href="https://vk.com/wall162891802_1105">About the number of DSODLS of orders 1-10</a> (in Russian).
%H A333367 E. I. Vatutin, <a href="http://evatutin.narod.ru/evatutin_dsodls_1_to_10.zip">List of all main classes of doubly self-orthogonal diagonal Latin squares of orders 1-10</a>.
%H A333367 E. I. Vatutin, <a href="http://evatutin.narod.ru/evatutin_dls_spec_types_list.pdf">Special types of diagonal Latin squares</a>, Cloud and distributed computing systems in electronic control conference, within the National supercomputing forum (NSCF - 2022). Pereslavl-Zalessky, 2023. pp. 9-18. (in Russian)
%H A333367 E. I. Vatutin and A. D. Belyshev, <a href="http://evatutin.narod.ru/evatutin_sodls_and_dsodls_1_to_10.pdf">About the number of self-orthogonal (SODLS) and doubly self-orthogonal diagonal Latin squares (DSODLS) of orders 1-10</a>. High-performance computing systems and technologies. Vol. 4. No. 1. 2020. pp. 58-63. (in Russian)
%H A333367 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 A333367 <a href="/index/La#Latin">Index entries for sequences related to Latin squares and rectangles</a>.
%e A333367 0 1 2 3 4 5 6 7 8
%e A333367 2 4 3 0 7 6 8 1 5
%e A333367 4 6 7 1 8 2 3 5 0
%e A333367 8 3 5 6 0 7 1 2 4
%e A333367 7 8 1 4 5 3 0 6 2
%e A333367 3 7 0 2 1 8 5 4 6
%e A333367 1 5 4 7 6 0 2 8 3
%e A333367 5 0 6 8 2 1 4 3 7
%e A333367 6 2 8 5 3 4 7 0 1
%Y A333367 Cf. A333366, A287761.
%K A333367 nonn,more,hard
%O A333367 1,4
%A A333367 _Eduard I. Vatutin_, Mar 17 2020