This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A215297 T(n,k) = number of permutations of 0..floor((n*k-2)/2) on odd squares of an n X k array such that each row and column of odd squares is increasing. 5
 1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 6, 6, 6, 1, 1, 10, 30, 30, 10, 1, 1, 20, 70, 280, 70, 20, 1, 1, 35, 420, 2100, 2100, 420, 35, 1, 1, 70, 1050, 23100, 23100, 23100, 1050, 70, 1, 1, 126, 6930, 210210, 1051050, 1051050, 210210, 6930, 126, 1, 1, 252, 18018, 2522520, 14294280 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Table starts .1...1.....1........1...........1..............1.................1 .1...2.....3........6..........10.............20................35 .1...3.....6.......30..........70............420..............1050 .1...6....30......280........2100..........23100............210210 .1..10....70.....2100.......23100........1051050..........14294280 .1..20...420....23100.....1051050.......85765680........5703417720 .1..35..1050...210210....14294280.....5703417720......577185873264 .1..70..6930..2522520...814773960...577185873264...337653735859440 .1.126.18018.25729704.12547518984.48236247979920.43364386933948080 Even columns match A215292. The first column is number of symmetric standard Young tableaux of shape (n), the second column is number of symmetric standard Young tableaux of shape (n,n) and the third column is number of symmetric standard Young tableaux of shape (n,n,n). - Ran Pan, May 21 2015 LINKS R. H. Hardin, Table of n, a(n) for n = 1..1000 Hodge, Jonathan K.; Krines, Mark; Lahr, Jennifer, Preseparable extensions of multidimensional preferences, Order 26, No. 2, 125-147 (2009), Table 1. Ran Pan, Exercise P, Problem 4, Project P. FORMULA f1=floor(k/2), f2=floor((k+1)/2), f3=floor((n+1)/2), f4=floor(n/2); T(n,k) = A060854(f1,f3)*A060854(f2,f4)*binomial(f1*f3+f2*f4,f1*f3). EXAMPLE Some solutions for n=5, k=4: ..x..0..x..4....x..0..x..1....x..1..x..3....x..0..x..6....x..0..x..1 ..1..x..2..x....4..x..7..x....0..x..8..x....3..x..5..x....3..x..7..x ..x..3..x..8....x..2..x..3....x..2..x..5....x..1..x..7....x..2..x..5 ..6..x..7..x....5..x..9..x....4..x..9..x....4..x..9..x....6..x..8..x ..x..5..x..9....x..6..x..8....x..6..x..7....x..2..x..8....x..4..x..9 CROSSREFS Column 2 is A001405. Column 4 is A215288. Column 6 is A215290. Sequence in context: A216956 A285522 A181039 * A225910 A215292 A124975 Adjacent sequences:  A215294 A215295 A215296 * A215298 A215299 A215300 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Aug 07 2012 STATUS approved

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

Last modified October 13 19:35 EDT 2019. Contains 327981 sequences. (Running on oeis4.)