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, 6, 68, 1670, 67295, 3825722, 285667270, 26889145828, 3102187523467, 429700007845870, 70303573947346474, 13405343287124139802, 2945521072579394529097, 738633749151050116349946, 209620243382776121032416188, 66830750007674204750148252472, 23780886787936166425634118631117
Offset: 1
Keywords
Examples
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;
-----------------------------------------------
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.