cp's OEIS Frontend

A337302 Number of X-based filling of diagonals in a diagonal Latin square of order n with the main diagonal in ascending order.

%I A337302 #39 Apr 15 2023 17:25:09
%S A337302 1,1,0,0,4,4,80,80,4752,4752,440192,440192,59245120,59245120,
%T A337302 10930514688,10930514688,2649865335040,2649865335040,817154768973824,
%U A337302 817154768973824,312426715251262464,312426715251262464,145060238642780180480,145060238642780180480
%N A337302 Number of X-based filling of diagonals in a diagonal Latin square of order n with the main diagonal in ascending order.
%C A337302 Used for getting strong canonical forms (SCFs) of the diagonal Latin squares and for fast enumerating of the diagonal Latin squares based on equivalence classes.
%C A337302 For all t > 0, a(2*t) = a(2*t+1).
%H A337302 S. Kochemazov, O. Zaikin, E. Vatutin, and A. Belyshev, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL23/Zaikin/zaikin3.html">Enumerating Diagonal Latin Squares of Order Up to 9</a>, Journal of Integer Sequences. Vol. 23. Iss. 1. 2020. Article 20.1.2.
%H A337302 E. I. Vatutin, <a href="https://vk.com/wall162891802_1291">About the number of X-based fillings of diagonals in a diagonal Latin squares of orders 1-15</a> (in Russian).
%H A337302 E. I. Vatutin, <a href="https://vk.com/wall162891802_1293">About the a(2*t)=a(2*t+1) equality</a> (in Russian).
%H A337302 E. I. Vatutin, A. D. Belyshev, N. N. Nikitina, and M. O. Manzuk, <a href="http://evatutin.narod.ru/evatutin_dls_scf_gen.pdf">Use of X-based diagonal fillings and ESODLS CMS schemes for enumeration of main classes of diagonal Latin squares</a>, Telecommunications, 2023, No. 1, pp. 2-16, DOI: 10.31044/1684-2588-2023-0-1-2-16 (in Russian).
%H A337302 <a href="/index/La#Latin">Index entries for sequences related to Latin squares and rectangles</a>.
%F A337302 a(n) = A337303(n)/n!.
%F A337302 a(n) = A000316(floor(n/2)). - _Andrew Howroyd_ and _Eduard I. Vatutin_, Oct 08 2020
%e A337302 For n=4 there are 4 different X-based fillings of diagonals with main diagonal fixed to [0 1 2 3]:
%e A337302    0 . . 1   0 . . 1   0 . . 2   0 . . 2
%e A337302    . 1 0 .   . 1 3 .   . 1 0 .   . 1 3 .
%e A337302    . 3 2 .   . 0 2 .   . 3 2 .   . 0 2 .
%e A337302    2 . . 3   2 . . 3   1 . . 3   1 . . 3
%Y A337302 Cf. A000316, A309283, A274171, A337303.
%K A337302 nonn
%O A337302 0,5
%A A337302 _Eduard I. Vatutin_, Aug 22 2020
%E A337302 More terms from _Alois P. Heinz_, Oct 08 2020
%E A337302 a(0)=1 prepended by _Andrew Howroyd_, Oct 09 2020