The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A337302 Number of X-based filling of diagonals in a diagonal Latin square of order n with the main diagonal in ascending order. 3
 1, 1, 0, 0, 4, 4, 80, 80, 4752, 4752, 440192, 440192, 59245120, 59245120, 10930514688, 10930514688, 2649865335040, 2649865335040, 817154768973824, 817154768973824, 312426715251262464, 312426715251262464, 145060238642780180480, 145060238642780180480 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS 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. For all t > 0, a(2*t) = a(2*t+1). LINKS Table of n, a(n) for n=0..23. 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!. a(n) = A000316(floor(n/2)). - Andrew Howroyd and Eduard I. Vatutin, Oct 08 2020 EXAMPLE 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 CROSSREFS Cf. A000316, A309283, A274171, A337303. Sequence in context: A222426 A107053 A327303 * A351349 A222271 A068376 Adjacent sequences: A337299 A337300 A337301 * A337303 A337304 A337305 KEYWORD nonn AUTHOR Eduard I. Vatutin, Aug 22 2020 EXTENSIONS More terms from Alois P. Heinz, Oct 08 2020 a(0)=1 prepended by Andrew Howroyd, Oct 09 2020 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 1 04:44 EST 2023. Contains 367468 sequences. (Running on oeis4.)