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A347927 a(n) is the number of reduced Latin trapezoids of height 3, whose top row has n boxes, the middle row has n+1 boxes, and the bottom row has n+2 boxes. 1
1, 6, 68, 1670, 67295, 3825722, 285667270, 26889145828, 3102187523467, 429700007845870, 70303573947346474, 13405343287124139802, 2945521072579394529097, 738633749151050116349946, 209620243382776121032416188, 66830750007674204750148252472, 23780886787936166425634118631117 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Peter Luschny, Table of n, a(n) for n = 1..100. Data from George Spahn and Doron Zeilberger, see link.

George Spahn and Doron Zeilberger, Automatic Counting of Generalized Latin Rectangles and Trapezoids, Enumerative Combinatorics and Applications, 2:1 (2022).

George Spahn and Doron Zeilberger, Latin trapezoids with three rows, the first 100 terms.

George Spahn and Doron Zeilberger, Latin trapezoids, a Maple package.

EXAMPLE

There are 6 reduced Latin trapezoids of height 3 with base of length 4:

----------------------------------------------

    2, 3;       |    4, 3;       |    2, 3;

   3, 1, 2;     |   3, 1, 2;     |   3, 4, 1;

  1, 2, 3, 4;   |  1, 2, 3, 4;   |  1, 2, 3, 4;

-----------------------------------------------

    2, 1;       |    2, 3;       |    2, 3;

   3, 4, 2;     |   3, 4, 2;     |   4, 1, 2;

  1, 2, 3, 4;   |  1, 2, 3, 4;   |  1, 2, 3, 4;

-----------------------------------------------

CROSSREFS

Cf. A002860 (Latin squares), A000186, A001623, A001626.

Sequence in context: A140606 A014505 A274722 * A127184 A333795 A113692

Adjacent sequences:  A347924 A347925 A347926 * A347928 A347929 A347930

KEYWORD

nonn

AUTHOR

Peter Luschny, Oct 22 2021

STATUS

approved

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Last modified January 22 01:28 EST 2022. Contains 350481 sequences. (Running on oeis4.)