A215290 -id:A215290 - cp's OEIS frontend

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.

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

Offset: 1

R. H. Hardin, Aug 07 2012

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

			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

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.

Column 2 is A001405. Column 4 is A215288. Column 6 is A215290.

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).

cp's OEIS Frontend

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.

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