A001627
Related to Latin rectangles.
Original entry on oeis.org
1, 0, 2, 44, 1008, 34432, 1629280, 101401344, 8030787968, 788377273856, 93933191303424, 13350759115563520, 2231133728986759168, 433075048506207645696, 96617322164029448916992, 24549315871469898190266368, 7047652261245574026565877760
Offset: 1
- S. M. Kerawala, The enumeration of the Latin rectangle of depth three by means of a difference equation, Bull. Calcutta Math. Soc., 33 (1941), 119-127.
- N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
A001624
Related to Latin rectangles.
Original entry on oeis.org
1, 5, 58, 1274, 41728, 1912112, 116346400, 9059742176, 877746364288, 103483282967936, 14581464284095744, 2419278174185319680, 466730664414683625472, 103580258158369503481856, 26198788829773597178540032
Offset: 2
- S. M. Kerawala, The enumeration of the Latin rectangle of depth three by means of a difference equation, Bull. Calcutta Math. Soc., 33 (1941), 119-127.
- N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
A001625
Related to Latin rectangles.
Original entry on oeis.org
2, 4, 60, 1276, 41888, 1916064, 116522048, 9069595840, 878460379392, 103547791177216, 14588580791234048, 2420219602973093376, 466877775127725240320, 103607067936116866084864, 26204424894484840874483712
Offset: 2
- S. M. Kerawala, The enumeration of the Latin rectangle of depth three by means of a difference equation, Bull. Calcutta Math. Soc., 33 (1941), 119-127.
- N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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.
Original entry on oeis.org
1, 6, 68, 1670, 67295, 3825722, 285667270, 26889145828, 3102187523467, 429700007845870, 70303573947346474, 13405343287124139802, 2945521072579394529097, 738633749151050116349946, 209620243382776121032416188, 66830750007674204750148252472, 23780886787936166425634118631117
Offset: 1
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;
-----------------------------------------------
- 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.
Showing 1-4 of 4 results.