A337302 Number of X-based filling of diagonals in a diagonal Latin square of order n with the main diagonal in ascending order.
1, 1, 0, 0, 4, 4, 80, 80, 4752, 4752, 440192, 440192, 59245120, 59245120, 10930514688, 10930514688, 2649865335040, 2649865335040, 817154768973824, 817154768973824, 312426715251262464, 312426715251262464, 145060238642780180480, 145060238642780180480
Offset: 0
Keywords
Examples
For n=4 there are 4 different X-based fillings of diagonals with main diagonal fixed to [0 1 2 3]: 0 . . 1 0 . . 1 0 . . 2 0 . . 2 . 1 0 . . 1 3 . . 1 0 . . 1 3 . . 3 2 . . 0 2 . . 3 2 . . 0 2 . 2 . . 3 2 . . 3 1 . . 3 1 . . 3
Links
- S. Kochemazov, O. Zaikin, E. Vatutin, and A. Belyshev, Enumerating Diagonal Latin Squares of Order Up to 9, Journal of Integer Sequences. Vol. 23. Iss. 1. 2020. Article 20.1.2.
- E. I. Vatutin, About the number of X-based fillings of diagonals in a diagonal Latin squares of orders 1-15 (in Russian).
- E. I. Vatutin, About the a(2*t)=a(2*t+1) equality (in Russian).
- E. I. Vatutin, A. D. Belyshev, N. N. Nikitina, and M. O. Manzuk, Use of X-based diagonal fillings and ESODLS CMS schemes for enumeration of main classes of diagonal Latin squares, Telecommunications, 2023, No. 1, pp. 2-16, DOI: 10.31044/1684-2588-2023-0-1-2-16 (in Russian).
- Index entries for sequences related to Latin squares and rectangles.
Formula
a(n) = A337303(n)/n!.
Extensions
More terms from Alois P. Heinz, Oct 08 2020
a(0)=1 prepended by Andrew Howroyd, Oct 09 2020
Comments